How do pirates crack games without access to the source code?

'Most' DRM schemes used to protect games work by scrambling (encrypting) the actual game program. The program that you run therefore isn't the game itself merely a stub that performs the following:

1. Check that this is a genuine game and the user is allowed to run it
2. Decrypt the actual game program
3. Run the actual game

There are many methods crackers use to break the protection but one is similar to the following:

1. Install a genuine, licensed copy of the game
2. Run the game allowing it to decrypt itself in memory
3. Use a software tool to 'save' the unencrypted program code from memory to a file
4. Make the program executable and remove all the software 'tendrils' that the DRM leaves behind

No. 4 tends to be the hardest part and can often be a cause of controversy within The Scene. Sometimes cracks will be nuked because they fail to meet the required standard by cracking groups.