I think of the godmother of punk rock hair is British textile and fashion designer Zandra Rhodes. In the 1960s, she started taking her aniline fabric dyes to her hairdresser for him to use on her hair as the only colors you could get at the time were realistic hair colors. She figured they worked on protein fibers, so why wouldn't they work on hair (another form of protein fiber). Lucky for us, there are many products that are a lot safer and easier to use these days.
Out of all the crazy hair colors I've used over the years, my favorite is still Manic Panic out of NYC. I used to buy it at Tish & Snooky's (the creators of the product) store in NY when I was a teenager. But I've also used a whole bunch of other brands and I recommend you trying whichever has that perfect shade you want, or try a few to see if one brand takes better to your hair than another.
If you're doing a color that's in the blue/green/purple family, you're going to want to bleach your hair very blonde or white before you put the color on, to get a brighter and truer color appearance. If you are doing color in the red/orange/pink shades of the spectrum, you can often get away with lightening dark hair into the lighter redhead shades and not have to go blonde. If you have light hair to start with, you're ready to go already.
The color goes on best on freshly-washed but not conditioned hair. Conditioner can block the absorption of the stain. Using a hair dye brush (like a paint brush) works best. Don't get it on your skin, as it can be unbelievably hard to wash off. If you can heat your hair after applying the color creme, it will be absorb into your hair more. Wrapping it in plastic wrap and sitting with a hood or bonnet dryer on your hair is the best. After about 45 minutes, rinse and I mean, rinse really well. You want the water to run clear, or excess hair color can rub off during your daily activities or drip down your face when you sweat. Dry and style as usual, and go get 'em, rock star!