Most answers focus on the solution for teleportation, and I think the wormholes solution fits well for your requirements. This part is well covered by other answers so I will not go into it deeper.
My answer focuses on the training part. This was too long to fit in a comment, so I turned it into an answer.
Creating the wormhole entry and exit points could probably be done with molecules manipulation, the construct requires extreme energy input, which he could probably generate with his powers.
He could first learn to create a small construct in such a way that it covers a small distance like let's say enough to push a bug through and see it pop out 2 meters away. He could wreck his surroundings while doing so, being inexperienced.
With practice he would learn to generate entry and exit portals so that they match his body shape with molecular precision (so he gets to spend less energy), also he would control the side effects on the surroundings better.
You could even pop in some humor like him teleporting himself and getting on the other side naked, or him teleporting other people with the same effect. Then mastering the technique to include clothes.
Edit: you might want to read A.E. van Vogt's Non-A World (a three book series). It's about a guy who can teleport himself, or others (or the tail of a flying plane to destroy the said plane).