This is a sort of redundant skill since you can obtain a skeleton key that voids it, but for the sake of levelling up to the max, this can be a bit of a slow one. You will need a decent amount of lock picks in order to level up your lock picking skill. You are bound to break a lot of them as you attempt to unlock the more difficult locks. The harder the lock, the more points you get toward raising the skill level. You should always make sure you have lockpicks on you and attempt to pick the lock on every door you find, so long as you don’t get in trouble for it. If you find a bunch of jail cells with nothing inside, pick the locks anyway.
A very useful top for this is to find any city you like and pick every single lock you can find within the walls. Be careful of the guards of course as it is a crime to be picking locks. Once you have picked all of the locks, leave the city walls and wait for 24 hours. Once you come back, all the doors will be locked and you can pick them all over again. This will greatly increase the time it takes to increase your lockpicking skill in Skyrim.