When I started mining I got help so here's the return.
SHA-256 coins are useless to mine on normal computers, you will make almost nothing and waste money in power. You want to mine Scrypt coins, such as Litecoins. Coinwarz.com tells you which coins are best to mine, but it is volatile, and I recommend Doge coin as it is fairly stable right now. On my 6870 GPU I make about 2k doges a day which amounts to around 0.004 BTC.
Just look up a mining guide and follow the instructions, make sure you are doing it for scrypt coins. I don't have any links, but I use CGMiner (command line) and multipool.us pool. You will also need to optimize your gpu - this info can be found on the litecoin wiki under hardware comparisons (Google this). Lastly, you need graphics card drivers (duh, but I actually forgot this when I did it the first time and it fixed one of my issues).
Hope this helps!