OK, so you've found yourself an interesting rock and you want to know how to identify it. I am going to go ahead and assume that you haven't studied Geology before (apologies if that's an assumption too far).
The first thing you can do is to head to your local public library and find a basic "rocks, minerals and fossils" identification book, and try to match up what you have with something in the book. Most of these books will include some kind of description of the various tests you can do (Mohs Hardness Tests, Acid Tests, Flame tests etc).
A quick google search for the geology of the area in which you found the rock might also give you a good starting point. You are more than likely not going to find an exact match by doing this, but it will help later if you have some idea of what you might have. It also means that you will have to look at the rock critically and you'll gain far more for having tried to identify it yourself. (I work with helping ID fossils on a regular basis, and it's far more rewarding if the person who has found the fossil has some idea as to what they have, or at least a reason for their identification).
If that doesn't get you anywhere, you can turn to the internet, there are places such as the NHM's Nature Plus where you'll find other people including experts and amateur rock hounds who might be able to give you more help. You will want to have good photographs with a scale (coins, Lens Cap, Rulers all apply).
If all else fails, Head to your local museum with a geological collection and look at the collection. You can also ask to speak to a geological curator and they should be able to help you identify your specimen (as your profile lists London as your location, the Natural History Museum's Angela Marmot Centre, The Horniman Museum, or British Geological Survey are all good bets).
