First off, wash your hair with a stripping sham[poo for a few weeks, and use lots of strengthening and moisterising treatmentss on it. Good shampoos for stripping are things like Head and Shoulders like alexa said, washing-up liquid, and a favourite of mine is baby shampoo - that no-tears formula strips colour out without stripping it of moisture too.
Once you've been doing this for a few weeks, it'll probably have faded as much as it will without using chemicals - and hopefullly, with regular intensive treatments it'll be in better condition too. If it's still not the colour you would like it to be, then you will have to use something stronger.
I personally can't say i trust home bleaches - you don't know how strong they are, so they could really damage your hair, so your best bet, i would say, ifs to go to a salon. If you're worried about the cost, ask in your local salons about Training Days or Evenings - these are much cheaper, and whilst the girl doing your hair won't be a pro yet, she will be supervised by one of the top stylists, so it's actually like they're doing your hair.
You have two ways to go about this, you could either gradually get more and more highlights, to gradually lighten your hair, and get semi permanent colours put over to tone down the lightened parts (the chances are, where your hair was black, it'll lighten to orange, and where you have regrowth it'll lighten to blonde, so youll need something put on to even that out). If highlights aren't what your after, asl about having a bleach bath - this will involve using a stripping shampoo with bleach in it to gently strip some colour out, usually out of the ends, leaving you with a lighter base to put another colour onto.
Generally I'd recomment highlights - it's a bit gentler on your hair. But the best thing to do is go to your local haur salon, ask about it, and they'll probably take a strand test, so you can see how well your hair will lighten up, as everyone's hair is different - yours might be fine.