Characters earn very little experience in Honkai: Star Rail just through playing. You’ll have to spend Character EXP materials to increase their levels. These materials include books called Travel Encounters, which give 1,000 EXP, Adventure Log (5,000 EXP) and Traveller's Guide (20,000 EXP). You can earn them by completing missions and taking on activities in the Simulated Universe and Calyxes.