so what exactly do I have to do to learn how to lockpick in Elder Scrolls Arena? I'm playing a knight.

Lockpicking is solely based off your class, level, and stats.

Agility, Intelligence, and Luck are the stats that matter for lockpicking. Note that Agility is actually a really important stat for nearly every character, as it affects melee accuracy, armor rating (your chance of dodging enemy attacks), as well as lockpicking and stealing.

As a knight, you do not get any class bonus to lockpicking, but you can still pick locks reasonably well if your level is high enough and you raise the relevant stats.

(By the way, for Arena, I really do recommend playing a spellcaster as your first character; it gives you access to the Spellmaker, the most powerful feature in the game, and the game is much easier as one. When you're more experienced, it may be time to play as a non-spellcaster.)