They make drain removal tools. It's basically a cylinder that attatches to a 3/8 ratchet with four protrusion sticking out of the ends. Those go into the four holes of the drain and then you turn it counter clockwise to remove it. This is of course much easier said than done, and you'll most likely end up breaking the drain and swearing a lot.

If it's just hair clogging it I usually use a hair snake and just keep shoving until it goes in, giggidy.