You grab a piece of mining software (e.g.
GUIMiner), sign up at a mining pool and start to mine.
What if I want to solo mine? And doesn't GUIMiner only support Bitcoin?
Sorry, I was thinking about bytecoin (which is a direct clone of bitcoin), you can use GUIMiner for bytecoin.
So I've tried like 3 different alt-currencies, including Bytecoin, and GUIMiner keeps on saying 'nothing to mine on, exiting.'