A Free Colonist may learn skills, which will convert it into a specialist unit. For example, if the Free Colonist is equipped as a Soldiers or Dragoons and wins a battle, it has a chance to be upgraded to a Veteran Soldiers. A Free Colonist performing an outdoor labor has a chance of spontaneously becoming an expert in that job (the chance increases each turn the colonist continues performing the same task without switching).
If you prefer a bit less randomness in your skills, a Free Colonist may learn a skill by visiting an Indian tribe. Only the first visitor to each native settlement can learn a skill this way, so you may need to get there before your rival European nations do. Free Colonists may also learn skills from expert teachers in a Schoolhouse, College or University.