To train an epic level - simply train the appropriate first skill past a cap on either game. You will receive a message in orange indicating your success.
Each training level grants +001% to your base skill within that group. 200 epic levels grant a flat 20% bonus to the base skill within a group. You will also receive 2 random equipment pieces/lures for training an epic level. Costs of epic levels are quite high but are an effective end-game money sink.