How does a guided missile turn?

Answer 1

Guided missiles have small fins or wings attached to them, and use them to alter the aerodynamics of the missile, in the same way that a plane with wings (and aerilons/flaps) does. The difference is that in a missile, the small fins/winglets aren't providing lift of any sort (the missile body does that, combined with the very high thrust of the motor engine), and are merely steering.

So, a missile flies through the air using the same principles as an aircraft.