As the manual says (I think it was the manual, maybe it was the 'pedia):
Training with the natives is a way to get specialists. Each native city has one specialist ability they will train, and one resource they want (each city, not each civ). To figure out which they want, send a person to the native city to talk to the ruler (you usually get a bonus as well for visiting them). Then, you will know what they train and what resource they want to trade. To train with the natives, send the person you want to train there (colonists train fastest, criminals slowest, servants in between) and the option will appear. Each city is different -- look for the natural resource you want.
I have found in one game I made the most use of this, that the very people I couldn't get from Europe, I could get from some natives. It may be coincidence, or it may be balance. Of course, once you get one, you can either send another to train, or you can go the schooling route.