Many towns have specific buildings you can train in. Go to such a building, and the Info button by each character will change to Train. Note that, in addition to skill points, training costs money. (Exception: Luck costs no money to train in, but still costs skill points. Don't let the lack of a monetary cost scare you; Luck is one of the best defensive skills.)
If you follow the road west from Fort Avernum, the first town you reach (by the bridge to the south) has a place you can train.