"A subtle and proud art... But long since rendered obsolete by the BROAD AXE!!! *slam*"
With the Lockpicking skill you can open chests in Dungeons, Prisoner Camps, Paragon Chests, Treasures you dig up from completing treasure maps or simply steal from the locked away supplies from the various NPC shops in town.
While you can train lockpicking the traditional way, UOPhoenix gives means to train the skill in a very short time.
Head towards Skara Brae to the House of Lockpicking.
There you will find tables with chests on it, with a little sign on them showing you the skill level of the chest required. There is also a NPC called Casey which will train you in various thieving skills including Lockpicking for a few hundred gold coins.
Once you're ready to start, simply lockpick any chest that matches your skill level. In example if Casey trained your Locpicking skill to 30, start with the boxes on the "Level 30" table, when you hit 40 Lockpicking move onto the next table in line (40). You will need approximately 250 to 350 lockpicks to train from 30-100
Note that you do not have to cycle through all the boxes on the table, simply keep opening one and when you succeed it will instantly magically close again, giving you another oppertunity to pick it.