WARNING
I'm not a hair dresser, stylist or technician. While I do understand how the process work and I dyed my hair a lot, I might be wrong on a few things. If you have questions or needs precisions, please make your own research. This page is about hair bleaching, coloring, their risks and tips, this is not a guide to help you choose which color should you dye your hair.
⇒ The most important general adivce : keep in mind that, as long as your scalp is fine, your hair will grow back, even if they're fried and break. I understand that hair is important but as long as you don't go overboard with these produces, you will be fine.
⇒ If your hair's health is extremely important, you have to understand and accept that bleaching will damage your hair. Most of the times, it can be fixed easily and quickly and the breakage is very mild, but little damage doesn't mean no damage.
⇒ Hair dye (permanent and semi permanent) will dye your skin, clothes, towels and even walls and floors if it touches it. Bleach can bleach your skin, clothes, towels and even your walls and floors if it touches it and stays on for even a few seconds. Protect everything you don't want to ruin, don't wear clothes you don't want to stain or bleach.
⇒ Do NOT metallic tools and containers when using bleach and/or developer. Do not use tools, ustencils and containers you will eat in neither, as there will be traces of produces in your food, even if you clean them well.
⇒ Brushes, foils and caps aren't mendatory, you can not use them just fine. Gloves, however, are very important to wear. While a bit of bleach or dye won't kill you and poison you on the spot, their traces are hard to remove.
⇒ It's always better to have too much than too little. Too little bleach will give you a mediocre, uneaven result, while too much bleach means you have to throw some away.
⇒ No, you can't mix your bleach and developer and keep it for later. Recycling is good, but this is dangerous.
⇒ And finally, it's always better to ask questions to a hair dresser or haircare shop keepers. I don't know if your hair is too fragile to bleach, or how much produces you should use, but they will. I'm not a professional, just a dude on the internet who dyes his hair often.
Produces
⇒ Developer : It's a liquid, usually white and thick, sold in bottles. It is used for premanent hair dyes, bleach powder and toner (though it is also used for other hair-related produces). Developer has a number of "volumes", which represents how strong it is, as 10 is the lightest while 40 is the strongest. I suggest you don't use 40 volumes, it's very risky, and might at best fry your hair, at worst cause chemical burns.
⇒ Bleach powder : Like its name said, it's a power. Usually blue, purple or white, it is mixed with developer to create a thick paste used to bleach one's hair. It works by opening the hair's follecules, oxidize melanin, and turns it lighter.
⇒ Hair dye remover : This powder, when mixed with developed, is used to remove artificial, and only artificial pigments. it doesn't bleaches or removes natural hair.
⇒ Permanent hair dye : Sold in a tube, it is mixed with developer and applied on one's hair to change its color. Like its name says, it is permanent, as once it's processed in the hair, it stays in place no matter how much you rince or wash your hair.
⇒ Semi-permanent hair dye : Sold in tubes, bottles or jars, it doesn't need developer. You apply it on bleached or very light hair, and it slowly fades with each wash. Depending on the dye, pigment concentration, and brand, it might last longer or not.
⇒ Toner : It is used to change the tone (aka how "warm" or "cold" your hair's undertone is) with a small amount of pigment. Red and orange pigments will make it look warmer, while green, blue and purple pigments will make it look colder. It is often use for bleached blond hair to make it look more neutral toned.
⇒ Other produces and tools : While there's no specific tool you have to get, there are some rules and recommandations : Do not, and I mean, do NOT use any metalic tools and containers, especially if you use bleach and/or developer. Do not use ustencils you need to eat with (even if you clean them well). You will stain and bleach your clothes and towels by accident, so don't wear and use anything you don't want to mess up.
Hair terminology
⇒ Hair level : From 1 to 10 (rarely 11), it's about how light your hair is. 1 is black, 10 is light blond and 11 platinum blond or white. Note : bleached blond hair and natural blond hair might look different, keep in mind that you might have to tone your freshly bleached hair.

⇒ Tone : Hair color's tone is about how "warm" or "cold" it is. Warm hair colors tends to look more red, orange, yellow and sometimes magenta and chartreuse. On the other hand, cold hair colors tends to look more green, teal, blue and purple. It also applies to browns and blonds : a warm brown would be chocolate, while a cold brown would be wenge.
⇒ Complimentary color : They're colors that compliments and neutralised another. Depending on what tone your current hair tone is, you might need a different toner. If your hair is more orange, you'll need a blue toner. If it's yellow, you'll need a purle/violet one.

Bleaching, Dyeing and Toning
Bleaching your hair means to apply a mix of bleach power and developer to oxidize (aka "rust") the melanin in your hair, making it look lighter. Depending on the level of the developer, ratio and time left to process, your hair might look lighter or darker. While it is possible to get blond hair with one application, if your hair is darker, it'll take two or three rounds.
Bleach will damage it, even if you're carefull, because you need to damage it to lighten them. To reduce breakages, you can use hair conditionner afterwards. I highly recommend that you bleach your hair when it's dirty, unwashed for a few days, as the natural sebum will protect your scalp. You can damage your hair all you want and it'll grow back. Damage your scalp and that's when you can get premanent damage to your hair growth. You can also use vaseline along your hair line and back of your neck to protect it from bleaching your skin.
Usually, you can mix your bleach powder and developer with a 1:1 to 1:2 ratio. You can use either, but if you want to go directly from black/brown to blond, use the 1:1 ratio. Anything lower (like 2:1) will make the bleach too strong or too dry, and anything higher (like 1:3) will dilute your bleach too much. Keep in mind that bleach will also bleach other things like clothes, towels and even your walls and floor, so be carefull and try to protect your surrounding (especially if you have long hair).
I recommand using a 20vol developer for any sort of hair color and bleaching, as it's a good compromise between damage control and power. After applying the bleach, don't touch them for about 30 minutes, even though you can wait up to 50 minutes if your hair is healthy enough. While you can use hair caps and foil, I don't recommand using them. It's not mendatory, and you should avoid speeding up the process. When you rince it, avoid using hot water, keep it luke warm at most, and the best would be slighly colder than lukewarm.
I'll go quickly on bleach bath. They're quick processes using bleach, developer and shampoo used to remove a bit of pigment, artificial or natural. The pause only last for about 5 to 10 minutes. They're less damaging but way less powerfull than normal bleaching, and should be used on damp hair only.
Permanent hair dye is a mixture and technique used to dye your hair "permanently". It is actually not completly permament, as it can be removed (though it's difficult) and your hair will keep growing with its natural color. You usually find permanent hair dyes in tubes, which you have to pierce and pour in a bowl. Then, you mix developer, apply on your hair like bleach, and leave it for about 35 minutes.
Most permanent hair dye should be mixed 1 part dye and 1 part developer. Most of these dyes stays on the range of natural hair colors, like blacks, browns, and blonds. Blond hair dyes won't bleach your hair, they mostly serve as toners.
While there are unnatural permanent hair dyes, they stick to shades of red, mauve, oranges and greys, and almost never blue or green. I don't recommand using these hair dyes if you aren't 100% sure you want your hair to stay a specific color.
Semi permanent dye is a hair coloring produces used to color one's hair without using developer. There are a lot of brands making them, and each have their own shades of colors, texture, smell, quantity and how they're sold. The most popular ones are : manic panic, crazy color, arctic fox, lunar tides, and lime crimes. While some can be bought on physical stores, all of them can be purchased online either on their website or in hair care/cosmetic stores (here in France, Bleue Libelule and La Boutique du Coiffeur). They all work the same, the differences are mostly related to color, pigment concentration, and ethic choises (vegan, not tested on animals, etc).
Usually, semi permament hair dye should be left on your hair for about 35 minutes.
Their advantages, compared to permanent hair dyes, it's that they slowly fade over time and are easy to remove. If you don't like this shade of pink, you can remove the pigment easily and try a new color. They also don't need developer. However, depending on the hair dye and how easily your hair keeps unatural pigments, certain colors or dyes might not work well on you or stay for more than a few washes, even if you bleached it white.
Concerning pastel colors, besides the mendatory "bleach it to level 10 to 11", you can make a pastel hair dye without buying a new bottle or jar. All you need is a medium (could be a clear version of your hair dye like with Manic Panic Pastelizer, or plain old white conditionner), and hair dye that is pigmented. If your dye is already pastel, don't try to dilute it even more. With your current color, let's say blue, all you need to do is add a bit of blue in your white conditionner. At most, don't go further than 1 part color, and 4 part dilutant, or there won't be enough pigment to actually color your hair pastel blue.
If you use semi permanent hair dye to cover another color, let's say green, be carefull on what color you want to achieve. If you use blue, your hair will turn a turquoise-blue. If you use pink or red, your hair will turn brown. You might have to bleach it or remove the artificial pigment, or use a very dark hair color like midnight blue or black.
There's no particular recommandations or brands you should avoid, since I have no bad experience with any of them. However, my favourite is Manic Panic. They're easy to dilute, has a pretty good price, they have a wide range of color, they're vegan and not tested on animals. They're also easy to find world wide as far as I'm concerned.
This section will be short as I never used toners before.
Toner is a produce used to alter the tone of your hair. For example, if you want white or grey hair, you have to tone it with a blue or purple toner. They're kinda like dye, but much diluted and specifically for changes the "temperature" of your hair (seek "Tone" in hair terminology).
Process
Before you even try to do anything, you have to understand that, even if you try to be as tidy as possible, something will stain. It could be your hands, ears, face, neck, clothes and more. Because of that, you have to prepare your enviroment.
Don't do anything in a tiny room, you will need space to move, especially if your hair is long. You can protect your floor, walls and even furniture with trash bags or plastic wraps (though trash bags are going to be less expensive). Let me tell you, bleach and dye stain, and stays forever on wooden floor, so protect them at all cost !
Your skin is also very likely to get stained : wear gloves and a tshirt you don't mind ruining. I insist on gloves, some people developped allergies to hair-care produces because they touched it too much, and hair dye can stain for a while on your hands. If you want to protect your neck and hair line, vaseline is a very good produce to use.
Like I said in the beggining of this guide, do NOT use any tool or container that is metalic if you use developer. Plastic, glass and wood is fine (with a heavy preference on plastic). Also don't use anything you'll eat with.
Bonus : if you bleach your hair often, wear a face mask, this powder likes to float in the air and that shit fucking irritates your airway.
Mix your bleach and developper (recommanded : 20vol) in your bowl. It should have the consistency of cake batter or cement (can't find any better comparaison sorry). Apply the mixture on your hair and let it sit up to 50 minutes. I've seen many people not putting enough bleach, so I'm telling you, soak your hair in produce, it should be completly wet and covered !
While it sits, don't try to use a blow dryer or something that'll heat up your bleach. Yes, hair dressers do that, but you aren't a hair dresser, and you definitively don't want to speed up a process that can damage your hair and scalp very badly. Foils, caps and plastic wraps aren't a bad idea, but be careful with them : they'll trap your natural body heat inside which will speed up the process. You can check from time to time to make sure the color suits your needs, it won't ruin anything if you wipe a bit of bleach off your hair then reapply.
When the time runs out, you have to rince it out fully. You can use shampoo to remove the bleach. Temperature wise, don't go any warmer/hotter than lukewarm, as your scalp is very sensitive right now.
Even if it's clean, some bleach may still sit on your hair, therefore drying it with a towel might bleach you towel a little. Don't judge the result until it's fully dry, because wet hair will always appear darker than it actually is. Check how well your hair feel. Is it really dry ? That's normal. Does it break with the slightless pull ? That shouldn't be happening. Is your scalp still burning, bright red or even leaking fluid ? Go to a doctor right the fuck now ! That's chemical burn !!!
Once your hair is ready, you can apply your hair dye. If the dye is permanent, you don't need to do much. However, if your dye is semi-permanent, your hair should be clean and dry, or the dye won't penetrate your folicules well. Just like with bleach, soak your hair in the dye, do not leave any spots dry. If your hair isn't wet from the dye, add more dye. Then, you'll let it sit. Depending on how vibrant or dark your final results should be, you can go from 15 minutes (pastels) to 35 minutes (the most vibrant/dark color you can achieve).
Rince it well, be warned, that shit stains the living hell out of your bath tub or shower. Now, do NOT shampoo them straight away, unless you want the final result to look a bit lighter/faded. Leave your hair alone for a few days, and when you clean your hair, try to keep the water temperature low. Not ice cold, but cold enough. Use shampoos that has no harsh chemicals, to avoid opening the hair folicules even more.
Be warned, you'll have to dye your hair often if you use semi-permanent hair dye, as it fades over time (quicker or slower depending on the dye and how often you clean your hair). With permanent hair dye, it shouldn't fade, or very slowly.