Go to Faendal at riverwood, the wood elf that usually stands by the mill. Ask him to follow you, then ask him to train your archery. (Have some gold around at least to make your first purchase of training). Ask to borrow something and take his gold; it's not considered stealing. Now repeat this for plenty of skill. Note: You can only level archery 5 times per level, but you level up a bit every time your archery skill goes up. This will work with any trainer who can also be a follower.