How can a dentist fix a slight overbite?

Align or restore. An overbite measures the vertical relationship of the upper teeth to the lower teeth. An overjet measures the horizontal relationship of the upper teeth to the lower teeth. In an ideal bite, a patient should have some overbite and overjet. Your dentist will be able to evaluate your occlusion (or the way your upper and lower teeth fit together) to determine if is is dentally acceptable & esthetic.
Orthodontic Rx. Normal vertical and horizontal overbites are each about 2mm. If front teeth are out of position it sometimes means that back teeth are also out of position. Overbites can be corrected non-surgically (braces to move teeth where they fit and function best) or surgically (reshape). Ask your dentist to refer you to an orthodontic specialist for an evaluation.
I wouldn't. It depends on your definition of slight and overbite. Some can be treated orthodontically, and some can be treated with restorations. To me, slight overbite is normal, so i may not recommend anything at all!