Visit Faendal at riverwood, he's a wood elf that usually stands by the mill.

1. Ask him to follow you.
2. Then ask him to train your archery. (Have some gold around at least to make your first purchase of training)
3. Ask to borrow something and take his gold. It's not considered stealing.
4. Repeat 2 and 3 infinity times.

Note: You can only level archery five times per level, but you level up slightly every time your archery skill goes up.
Note: This will work with any trainer who can also be a follower.