1. There are stepper driver IC's.

2. You use transistors of MOSFETS... but you have to connect each stepper wire between two MOSFETs. One will drive that wire HIGH to V+ and the other drives the wire LOW to 0v.

The clever bit is that ONLY ONE can be switched on at a time. If you happen to switch both on, you'll get a dead-short across your supply, and your PSU or your MOSFETs will complain (usually loudly with accompanying smoke).