Some might call it cheating, but its neither a bug nor a glitch. It might just be something the developers overlooked or actually intended.
In the video above, QuebecGaming1 shows us how to level up your archery skill to level 50 without spending a single septim or firing a single arrow.
You need to recruit a character named Faendal. You can learn how to recruit him here.
The video explains it better, so just watch it and see your archery level go through the roof.