DB2 is different from some of the other RPGs in that regard. There is no training ground. Instead, head into the wilderness or the cellar to fight monsters. Every time you kill one, your party members gain experience. When you have enough experience, visit the Elder's Review Council in New Treleon, on the west of the center courtyard, to promote your party members. As they get promoted, they increase in attributes like strength and dexterity.