How do conventional missiles fly?
Air-to-Air guided missiles are little airplanes. If there are only fins at the tail, it's a ballistic rocket, basically a fin stabilized artillery shell accelerated by a rocket motor instead of an explosion in a pipe.

On missile like AMRAAM, Sidewinder, or Sparrow, the vanes are wings and the missile is a rocket powered aircraft that can climb, descend and turn as required.  The vanes/wings don't have to be very big because the thing is going superdupersonic.  The X plan form means the wings can support and control the missile equally well in any axial position.  

The front vanes are movable and do the controlling.  It's effectively a rocket powered robot canard aircraft on a suicide mission, really.

Since the missile accelerates to >Mach pretty quickly and operates supersonically, the wings/vanes use a supersonic airfoil profile, either biconvex (like the F-104's airfoil) or a diamond profile.  The vanes on the AIM-9M look like biconvex airfoils.

The missile descends when it is first launched because it's going too slowly for its teeny tiny supersonic wings to do enough lifting, and has to accelerate first.



Now, for a change of pace, slow something like an AMRAAM or Sidewinder down to subsonic speed, make the fins bigger and provide control surfaces on the rear ones, power it with a turbojet instead of a rocket except for boosting it into the air, and you have the CL-89 surveillance drone, basically a reconnaissance cruise missile that flies hither and yon at low level taking pictures.