A lot of people want to dye their hair with semi-permanent unnatural-color dye, such as Manic Panic, Special Effects, or Punky Color. Its actually quite a process and requires a lot of attention to detail or your hair will look/feel really bad, the color will not come out right, and itll fade instantly. This is, as far as I can tell, a definitive way to do it, from years of trial.

Step 1: Get Stuff

You'll need:

basic hair dying tools: combs, hair clips, a tinting brush, plastic bowls, rubber gloves, petroleum jelly, tin foil (you can get precut tinfoil at the beauty supply store or just cut some everyday kitchen foil)
bleach: BW2 or similar bleach powder, get two packets for short hair and a small bucket for longer hair. you really dont want to run out. peroxide developer (20 vol for light hair, 40 vol for dark hair) a small bottle (4oz) for v. short hair, a large bottle otherwise. its cheap stuff and you dont want to run out.
toner: "blue lightening"/"platinum"/etc. for dying hair a blue, green, purple, etc shade. "light blonde", etc for dying hair an red, orange, yellow shade. They come in 2oz brown bottles. ask the salesperson to point you to it so you dont get the similarly looking hair dyes. they're often apart and near the bleach.
hair dye: "special effects" is my favorite and seems to seep least and keep longest. however, "manic panic", or "punky color" is OK. get a couple similar shades to get a gradient effect. most hair can be done w/ a single bottle. if you have a lot of hair, get two shades to make sure you're covered. you'll also need some left over for touching up. some people use "kool aid", but i cant advise it I buy mine from the garment district, which also sells online. any reputable place will have a color swatch panel. If you happen to have some hair bits, say cause you just cut your hair or something, you can dye them to get a sense of how it will come out.
other: j&j baby shampoo, hot oil treatment, an old/unwanted towel that you can use to dry your hair once its dyed

You can't get most of this stuff at a generic drug store, especially the bleach and toner... you must go to a beauty supply store!

Step 2: Bleaching

cut the tinfoil into small squares.
wash & towel dry your hair.
mix up the bleach powder and developer in a plastic bowl with the tint brush, i feel like its a 'frosting' consistancy.
both people should wear old clothing as bleach will immediatly damage anything it touches.

Starting at the back of the head and moving up to the crown (this is very important!) The person bleaching the hair divides up the hair into chunks and brushes the bleach into the hair, get close to the roots but dont get the bleach on the scalp because it will itch a lot.

After each chunk of hair, fold it into the foil. my lovely assistant crunched the foil, but thats not advisable as its harder to remove without yanking the rather delicate hair

Step 3: Wash Out Bleach

Depending on your natural hair color (mine is dark blond), your desired color (a medium red), and developer (20vol) you wait 20-30 min or so and then wash out the bleach. i think using a hair dryer on warm will speed it up, but thats just a guess. take out a foil and see if your hair looks good. then wash it out completely. because its just a bleach step, hair will be 'brassy'

Step 4: Tone

Toner takes out the brassy color and leaves hair white-ish (blue toner) or blond (gold toner). Its also a mild bleach.

Mix the bottle with peroxide (50/50) and apply to hair with the tint brush, back to front. I think you can foil but I tend not to. After 20min, wash out.

Step 5: Dye

Finally, with all the prep done, pour out the dye(s) into plastic cups and decide what color should go where. Some people like to have bangs or streaks a seperate color, or fade from back to front or from roots to tips. I wanted a "fall leaves"/"flame" effect so we just alternated shades.

Before you start, rub petroleum jelly along your hairline: the dye will stain your face and ears if it drips or rubs, and its rather hard to remove.

Dye hair from back to front, make sure the hair is saturated, and use a fine toothed comb or stiff brush to brush the dye into the hair. Get close to the roots but dont dye the scalp: it looks wierd.

Now cover your hair with a showercap if its long to keep it from getting all over the place. Some people use a hair dryer to speed this up, but I dont. Wait 30min-1hr to get a good set.

When you wash it out, try to do it in a slop sink or similar because the dye can stain the porcelin and its a pain to get out (softscrub/ajax seems to work well). wash away from the face and body so that the dye doesnt drip onto your skin and paint it. A wand is good here. Maybe have your friend help you out. Wash until the water is clear, 10min minimum...otherwise you will just get dye on everything.

The folks at haircrazy suggest a vinegar rinse to help set the color. this seems like a very good idea, but i didnt know at the time.

Step 6: Upkeep

After you've washed out the dye, you may want to consider doing a hot oil treatment or two because your hair is very damaged. The dye is a conditioner but I still think it helps.

When you wash your hair, use J&J baby shampoo which will not strip all the color out at once. Harsh shampoos will make the color fade within a few washes. Some people suggest using a "coloring shampoo" (from the beauty supply store) if one is available.

Dont forget to wrap your hair in the dye towel when you sleep (if its long) or cover your pillowcase (if its short)

You can do minor touchups every few weeks to keep it lookin' good!