Hi Claire! I get a biggish bin and fill it with very hot water and then dump in some chlorox bleach. I kindof play it by ear how much bleach to use - I generally use around what I use to turn DD's disgusting socks back to something approaching white. I also never bleach anything that's isn't linen or cotton. Note that some colors just will not bleach - some neony pinks and tans - so be prepared.
Put the item in clean and wet, and use enough water/bleach to cover the item completely. Swish it around, then let it sit until it's the color you want. Then dump out the bleachy water, and wash the item, using an extra rinse to get rid of the bleach smell.
If you wind up with any dark spots, you can use chlorox spray cleaner to take them out - but be warned, that stuff is STRONG so use caution and rinse right away! It's really best to use this if you've bleached your item to something close to white. (However, it might create an interest effect if used wisely, I haven't tried that yet!)
Also, word to the wise: don't do this with bare hands. My hands are still raw and cracked in the creases from not washing the bleach off fast enough when I transferred this skirt to the drier. Ick.