Lockpicking svcks in Daggerfall. It is difficult to train (you basically need to pay for training, and a lot of it, because it is so slow to develop on its own).
However, there are two other methods of bypassing locked doors: Basking and magic.
Bashing is done by just pulling out your weapon or fists and attacking the door. You'll make a lot of noise, and it does some serious wear on your weapon (so use your fists or carry a spare), but you can break open the door and let yourself in that way. Of course, doing this in town means you'll alert the city guards, but often that isn't such a threat.
Magic uses the Open spell from Mysticism. Even the lowliest open spell (1-2 + 1-2 per 2 levels) can open ANY external door in any city. Locked doors in dungeons may require more, but you can usually bash those if you can't get it, and if its a magically held lock you can usually find a switch nearby to take care of it.