Well, I did lots of gait work with runners. We started with some video run gait analysis, followed by some movement screening, checking range of motion, strength etc to get some additional insights into why they had compensations. Then we started working on mobility and stability through training. This is a LONG term process, years rather than weeks. Gait compensations are deeply ingrained patterns that are hard to break, even when you remove the need for compensation. It is worth working on though.
As for myself, I switched to very minimal shoes (Shamma running sandals actually) over a 5 year period, then worked on hip and glute strength, plus running posture.