EDIT: Updated for linux users.
What is BitCoin?
Refer to this website. Basically, it's a crypto currency that allows you to make virtual money using your GPU. You can mine solo or join a pool. The latter option is the norm since the difficulty of mining solo is beyond a joke.
Okay, so what GPU works better for mining?
ATI Radeon cards work really well for mining. nVidia cards don't have the guts involved for proper mining (they miss a critical instruction that ATI supports natively). I'm not going to go into the war between the two vendors but ATI cards are a massive gain over hashing on nVidia. I own a HD7970 myself. and it gets around 600Mh/s... while my GTX670M only gets ~55Mh/s.
Another dot point that you need to note is power consumption - since your GPU will be running at almost 100% usage, your graphics card can draw awful amounts of power. You also need to consider your power supply - my HD7970 requires 550W or greater, however I am running it on a 500W PSU. I have had random GPU resets that make the mining software stop in its tracks.
Okay, I sorta got that...
Sorry if I bamboozled you. Pretty much, if you have a modern day ATI card (4700+ onwards), you should be set. Make sure your GPU drivers are current. However, for ATI cards, newer drivers are a mess for mining! You're best to be on 11.6 for old 4xxx cards, 5xxx and 6xxx 12.6 and 7xxx 12.8 or 12.10. If you have a newer card, you can try mining but some drivers have a big impact on hashing performance. I am currently running 12.8. For nVidia, the current ones should do. Have a Intel HD Graphics card? Sorry, you're not going to be able to mine effectively.
Download the latest cgminer from the following URL, http://ck.kolivas.org/apps/cgminer/ . At time of writing the latest was 2.11.4. Grab the Windows build if you're on windows, if you're on Linux, grab the one for your arch - if you use Ubuntu and friends 12.10 and onwards you'll be able to use precompiled binaries as long the Linux AMD APP SDK is installed. Extract to a directory like C:\Mining .
** If you download the APP SDK, use SDK version 2.7 or eariler, 2.4 at the minimum. Version 2.8 is broken **
While you're there, READ THE README. I'll give you the base minimum you need to get started but for better tuning, you'll have to experiment. The best options are sometimes the defaults.
Now since you've extracted the cgminer build, you may get a virus warning. Set your antivirus to IGNORE the directory that cgminer is located in because it is NOT a virus. If it was, I wouldn't have written this tutorial, would I?
Now, you need a command prompt or a terminal. Open CMD on windows (you should be able to find that on Windows - if in doubt look for Command Prompt on Vista/7's start search or press CTRL+R and run 'cmd').
Winderp Windows 8 can get a command prompt by right-clicking the left most bottom corner and choosing "Command Prompt" from there.
Now, you'll need to change to the directory that the cgminer is located. For example, mine is at C:\Mining . So, I do this:
C: (if not already on C Drive) cd \ cd Mining cgminer.exe
Linux users can just extract, change directory and then do ./cgminer .
Now, you'll need a pool to mine with. I would suggest the friendly OzCoin pool. Alternative is 50BTC Once you have registered and logged in, go into the Worker section of your panel, and make a new worker. You should get a number like 19987 or something that is your worker ID. Look under that area, and you'll see server details. Make note of the one closest to you. For this case, I'm using au.ozco.in .
Back at the command line, you'll get something like this. Enter the pool url, username, password when prompted.
Started cgminer 2.13.4 Need at least one pool to mine with. Enter server details. URL: au.ozco.in:3333 (you can change this to us.ozco.in:3333 or eustratum.ozco.in:3333 if you like...) Username: 19987 (the number your worker ID is) Password: somepass (don't enter this, the password is the password is that you got on your worker page).
After pressing enter, cgminer will initialize itself and start mining. Now, it's time to leave the PC alone - interactions while mining will reduce hash rate. If you are using this setup as a dedicated setup, you can go into GPU management and change the intensity from it's suggested setting up to 11. Do not go over 11, you will get bad things happening. A recommended intensity is 9 for dedicated miners. The higher the setting, the system will be laggier to respond. To quit mining, press Q on the main menu.
There are many other options one can tweak but user tweaking often leads to bad things, other than cautious over clocking. When done, go to settings, write config file, press enter, and then press any key to return to the main menu. That allows you to run cgminer without having to set it up all over again!
I'm willing to help you but I need to know what the issue is. Also, please please please read the readme and understand that to the best extent possible that you can! It answers approximately 99% of your questions.
I'll do a Litecoin mining for dummies tutorial later, but for now, enjoy your bitcoin mining experience. Time is money.