Bsrhrki

With the exception of cruise missiles, most missiles don't have any obvious lifting device.

If you watch a missile being fired, prior to its rocket firing it does exactly what you'd expect: momentarily plummet toward the earth. And yet the moment it ignites, it stops falling completely, but without any pitch that you'd expect to counteract gravity; even big missiles like the Phoenix or HARM seem to have gravity-defying characteristics.

Missiles that fire on the rail seems to experience no drop at all.

AIM-9M launch from an FA-18F source

There's a good slow-motion video of the firing of an AMRAAM here.

Now this isn't magic, so I presume either a) the little fins make adjustments so that the rocket is, despite appearances, pointing a little downwards or b) the fins are smart enough to configure themselves to provide the lift needed to keep the missile in the air. But it might be neither.

The question is - generally, how do conventional missiles fly?

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.

The missile's wings are very large for it's mass, and produce a great deal more lift than the wings of the aircraft firing the missile.

One thing to note from the OP's linked video is that the F-35 and the chase plane are traveling at the same speed, so the F-35 appears stationary. However, that aircraft is likely traveling in excess of 0.8 Mach. Therefore, upon release, the missile is also traveling at 0.8 Mach. The large wings provide plenty of lift. Some missiles may thrust vector as well.