I Can withdraw my coins to an Address using Mt.Red, but I'm not quite sure where the wallet comes into play?
Your wallet contains the keys to your address(es), allowing you to spend coins sent to them. Click Recieve Coins in the client to see a list of your addresses. You will already have one address by default, and you can create as many more as you want.
I've talked about people backing up the wallet?
Because your wallet contains the keys needed to spend your coins, if you ever lose your wallet, you will lose the ability to spend your coins. This is why it is so important to back up your wallet. But before you do that, you should first
encrypt your wallet, otherwise anyone who manages to gain access to your wallet will be able to steal your coins. Once your wallet is encrypted, a passphrase is required to spend your coins (but
do not forget your passphrase - if you do, you won't be able to spend your coins).
After i withdraw my coins to at address using Mt.Red, what do I do next?
Once the coins are in your wallet, you can do whatever you want with them. Buy things with them, donate them to charity, sell them for dollars, whatever. When whoever you're doing business with is ready to accept your bitcoins, they will give you a Bitcoin address to send your coins to. Click Send Coins in your client, enter the address they gave you and the amount of bitcoins then click Send. Easy as that.
And after that, how do I get my coins onto something link Mt.Gox as so then I can cash these coins out for $$
After you create an account on an exchange site, you will be given a deposit address to send your coins to.