What is the best way to correct muscle imbalances? For example, if you can do 10 one leg squats with your left leg but only five with your right, how should you go about correcting the problem?
Asymmetry in muscular strength is common. This may be caused by the joint on the weaker side may not be stable (i.e., hyper/hypo mobile due to overuse and/or injury). When this occurs, the body inhibits the strength of the prime movers around the joint so that they do not perpetuate any further damage to that joint.
If there was a past/present injury to the spine, there may be an electrical disruption in one or more of the nerve roots of the lower extremity musculature, again, inhibiting the strength of the prime movers. Other physiological factors such as disease and malnutrition may play a role as well.
If any of the above are suspected, it may be wise to refer your client to the appropriate specialist (i.e., DC, PT, ND, OCS).
However, assuming your client is of average health and is pain and disease free, your training protocol must begin with a thorough assessment. Drastic strength differences like the one you're noting will undoubtedly manifest/expose themselves as some sort of muscular length/tension imbalance(s). This in turn will be evident in shape or form in their static and/or dynamic posture(s). Essentially, you as the exercise professional must facilitate or trigger the weaker/longer muscles, and likewise, inhibit or quiet the tight/short muscles. (NOTE: In terms of length/tension, a muscle will have less than optimal strength whether it is too long OR too short.)