What is the procedure for correcting overbites via teeth distraction?

Orthodontic movement: I assume you mean "teeth extraction". Often in adults removal of teeth is necessary to allow movement of other teeth into better occlusion. In the growing child we can mold jaw size and position. In the non-growing adult, short of jaw surgery, we are limited to tooth movement to resolve a malocclusion (bad bite).

you mean extraction: If your talking about extractions , its an orthodontic that requires the removal of teeth usually premolars and moving the remaining teeth back into alighment. Another way to do this is to expand the palate move the teeth in. If your overbite is too extream for this to work you might need cosmetic/restorative dentistry to correct the problem.

Moving jaw: Distraction osteogenesis can be used to gradually move the upper jaw (maxilla) forward to correct an "underbite" or class iii occlusion. It is done in cases where orthodontics alone, or traditional oral surgery cannot move the jaw enough. It us used for patients who have more than 1 cm underbite. It has nothing to do with extractions.