You only need a few things:
A colored t-shirt
A spray bottle that sprays a fine mist
A small plastic bucket that is about as big around as your shirt's collar
String, yarn, or heavy thread
1/3 cup (79 ml) of chlorine bleach
4 cups (1 liter) of vinegar
Step 1: Select Your Shirt
Red will usually turn pink, sometimes white.
Orange most often ends up a lighter shade of orange.
Yellow will usually turn white.
Greens will turn a light yellowish green or white.
Darker blues turn red or pink. Lighter blues turn white.
Purple will almost always end up pink.
Most black shirts will turn orange or red.
Gray and brown will usually turn pink.
White will turn... white. So don't use a white shirt. =)
The only way to be absolutely certain what color the shirt will turn... is to bleach it! If you're the cautious type, try cutting the sleeves a smidgen shorter and spraying the scraps with bleach. This is pretty much the only way you can "test" without bleaching your entire shirt, but of course you'll have shorter sleeves now!
The one I picked is a layered-look shirt that's purple on the top, and teal on the bottom.
Step 2: Dress the Bucket
Place the shirt around the bucket, as though the bucket is wearing your shirt. Tie the string tightly around the hem (bottom) of the shirt to hold it in place.
Step 3: Wrap the String Around the Shirt
When you run out of room to wrap the string, slide the part you've already wrapped down the bucket (towards the hem), and then keep wrapping. The shirt will wrinkle and the wraps will overlap each other, but that's what you want to happen.
When you get to the sleeves, just try to flatten them out the best that you can. Keep wrapping the string and sliding the wrapped portion of the shirt down until... you have no more shirt left to wrap! Tie the string off to hold everything in place.
Try not to have any wrinkles be too big or uneven, but don't stress out about it too much. It'll look great when we're done!
Step 4: Bleach It!
Now mix 4 cups (1 liter) of vinegar with 4 cups (1 liter) of water. Keep this separate from the bleach mixture, to use in a few minutes.
Make sure that you're outside and wearing old clothes for this next part: spray the wrapped shirt all over with the bleach/water mixture. Get it nice and wet, and let it sit there for 5 to 10 minutes. The color will get lighter the longer it sits, so let it sit longer if you want higher-contrast stripes. Don't let it sit for longer than 10 minutes, or you may weaken the fabric of the t-shirt.
Step 5: Use the Vinegar Mixture to Stop the Bleaching Process
After 5 minutes, rinse the shirt in plain water, and then run it through the wash like normal.