Look for videos on trouble-shooting such shifting problems. That said, the first things I looked at as a bike mechanic diagnosing such shifting problems were (a) inner and outer limit and cable adjustment (e.g., in case someone who didn't know better had monkeyed with those), (b) cable and housing condition (looking for kinks, grit, and lack of lubrication), and (c) derailleur hanger alignment (if the bike ever fell over on its right side, the hanger might have bent, resulting in a deterioration in shifting performance and the possibility of the derailleur running into and ripping out spokes and/or breaking the dropout and/or the rider crashing).