You cannot get the skill until late in the game, because the only place to learn the skill is in the Control Center, and entering that is a complex job. First you need to complete the Tomb of Varn and find 6 Code Scrolls, each of which contains a password. You will need these passwords to enter the trapdoor in the middle of the Well of Varn, which leads to the Well of Varn proper – and by the way, cast Feather Fall first! You will then need the find the Control Cube.
Then return to the Oracle, and click on the new option which has appeared. When you enter the Control Center, the blaster skill will be found by taking the 1st left from the entrance and click on the panel inside. Anyone can learn it. Please note that the Control Center is NOT a nice place, and contains enemies that can can destroy a full-strength character with one hit.
Trainers for Expert can be found in New Sorpigal and in Eel-Infested Waters, and the Master Trainer is (IIRC) in a house towards the eastern side of the village of Edenbrook in Paradise Valley.