How convection within the earth drives the movement if crustal plates and causes changes to earth's surface

Gosh. This is a relatively poorly understood area of geotectonics but the basic gist of it is that at divergent plate boundaries you have a lack of convective currents which results in an upwelling magma from the mantle. This process creates new crust and in response pushes the old crust forward as a rift is created. Because it is pushed the plate will eventually collide with another plate and sink underneath it resulting in orogenic processes (mountain building and earthquakes) on the surface of the earth.