The common approach for strength and conditioning for sport is to establish a baseline of strength and cardiovascular endurance separate from the sport, then work on sport-specific strength, endurance, and conditioning. Strength work is maintained while working on other attributes and tapered before competitions. I like Kurz' Science of Sports Training for specifics on this topic, though it may be too much detail not focused on tennis for your specific situation.
In addition to strength, you should consider the attribute of power, which is a separate quality that is derivative of strength. It is best developed by submaximal weights moved explosively. Cleans, snatches, jerks, and push presses are the most common techniques used. One should have a foundation of strength before focusing on power movements.
The first step is to take a novice resistance program such as Starting Strength. It may be necessary to modify its programming according to your sport schedule, but one to three strength workouts per week should be possible even around regular sport training. After you have a baseline level of strength--perhaps a bodyweight squat, greater than bodyweight deadlift, and the ability to do several pull-ups--it would be reasonable to look at tennis-specific strength and conditioning and power workouts. Some recommend even greater levels of strength, such as double bodyweight deadlifts and 1.5x bodyweight squats, before sport-specific movements should be incorporated.