It is easy to earn yourself some bitcoins by employing an idle gpu to do these hashes so you may have your piece of the Bitcoin pie.
The first step of getting on your way to earning bitcoins is getting a wallet. You have several options, but in this tutorial I will be walking you through the vanilla bitcoin-qt. You will want to acquire this by going to http://bitcoin.org/en/choose-your-wallet You can find a lot of interesting info on the official bitcoin website and if you are curious about the specifics of how it works, they have a very informative video on the front page that you may want to watch.
I drew an arrow to point out the bitcoin-qt icon. You can click on this to bring you to the download of the client. Download this and it should be your usual installation process that you are accustomed to in windows or mac or linux.
After you get it installed it should look something like this
Notice the green bar in the bottom that says 8 days behind. Your computer must download all of the block, the bits of data that your gpu will be calculating, before it is able to begin hashing.
After you get your wallet all set up you will want to go to http://guiminer.org/ to download your miner. This is the software that will get you set up to start hashing with your gpu.
Once you have downloaded and installed that you can open the app and it will look something like this
The first step in here will be to click "File" and then "New Miner". Then you will have four options. I Suggest OpenCL for anyone new to bitcoin. You can name the miner whatever you want.
Once you have your miner set you should go back to the bitcoin-qt client and you will want to find you address.
As you can see, it is on the right hand side under the receive tab. You will want to copy this and then paste it into where it says address in the guiminer app. The address is the location that bitcoins will be sent to and from for transactions. In this case it is used to receive your coins from mining.
Here is the finished miner set-up. Something you may notice is that I have changed the server from the default. I suggest using elgius because it doesnt require any account set-up, you may just put in your address and you will start getting paid. You can mess around with the cpu affinities to see what works out. This is a setting that will allow your miner to use certain cores of your cpu. Make sure that the gpu you want to use is selected and your address is in there and then you should be good to go. Hit start mining and then it will tell you your hash rate in the corner and it will tell you how many blocks you have processed