To improve your mercenary's dexterity and strength, you should perform hand-to-hand combat with the enemy (This is risky).

To improve your mercenary's marksmanship, perform long range shots at easy-to-kill areas (heads, body, etc.).

To improve your mercenary's medical skill, have the mercenary heal the other mercenarys repeatedly.

To improve your mercenary's leadership skill, have the mercenary train a militia.