First thing you need to do is get a Bitcoin Wallet. Because Bitcoin is an internet based currency, you need a place to keep your Bitcoins. Got to
http://www.bitcoin.org and download the Bitcoin client for your Operating System. Install it and click New to get your wallet ID. It will be a long sequence of letters and numbers. One of most important things you can do is make sure you have a copy of this on a thumb drive and print a copy out and keep it in a safe location. The reason is that if you computer crashes and you do not have a copy of your wallet ID, you will lose all of your Bitcoins. They wont go to someone else, they will disappear forever. It is like burning cash.
I want to make a correction here. Having a copy of your wallet "ID" (what you are talking about is actually your address) is not enough. You need to backup this file: C:\Users\YourUserName\AppData\Roaming\Bitcoin\wallet.dat. This file contains your private key as well as all your addresses. You cannot access any of your addresses (you can generate as many as you want) without the private key.