They, in turn, control exactly what your PC will do by issuing commands using a variety of means. It used to be that IM (instant messaging) like IRC (Internet Relay Chat) was the preferred way to do this. Lately, though, to avoid detection, they've taken to using social networking tools like Twitter.
Once in place, you can rip out botnet software with the anti-viral tools, but it can be a real pain. The better thing to do is to avoid getting a case in the first place. The Internet is a dangerous place, especially for Windows users, and practicing safe computing isn't just a good idea, it's a necessity if you don't want your PC to be dragooned into a botnet.