These are the skills that I most commonly classify as the "Thieving Skills": Sneak and Security.
You gain skill improvement points in Sneak by avoiding detection when a critter has the opportunity to detect you and by picking pockets. Picking pockets is worth 2.0 skill improvement points (base value) for each successful attempt. Avoiding detection is worth 0.25 points (base value) for each instance where you avoid detection.
The key to avoiding detection is that there must be something nearby that can detect you. But nowhere in the rules does it say that it has to be a hostile creature. One of the earliest tricks that I discovered was to simply walk into any tavern, station myself in a corner, tape down the <ctrl> key (don't know what it is on the Xbox version) and then go do something else for a couple of hours. When I came back, I had a serious skill increase.
The other little trick that I discovered was that Paralyzed creatures can still detect you, but can't do anything about it, so the detection script never activates. In effect, every attempt to detect failed. So I made a magic item (I used an Exquisite Ring and a Bonelord) that cast a targeted Paralyze for about 60 seconds. The next dungeon that I entered, I paralyzed every critter I came across, Sneaked up next to them, tried to pick their pockets, and then backstabbed them (for 4x damage with my handy Daedric Wakizashi). It seemed like every time I turned around I was getting "Your Sneak skill has increased" at the bottom of the screen.
The Ring of Paralyzation had a couple of unintended benefits. First, there is almost no hand animation associated with it, so you can shoot off the spell almost as quickly as you can click the mouse button. This often means that your spell hits the target while the target is still in the casting animation. An unintended benefit of this is that your spell can impact the target's spell before it reaches you, canceling both. Your spell is essentially running interference for you against magical attacks. But because you are casting faster than the target, your spell is going to get him eventually.
For Security, there is no trick. Just carry around lockpicks and probes. Unlock and disarm everything you come across that won't bring the guards down on you (unless you have a very high Sneak skill and can avoid detection while you're doing it). Because lockpicks and probes only have 25 uses, you'll need to carry several.
For safety's sake, I typically disarm first and unlock second. That way I don't set off the trap by inadvertently opening the item. At 2.0 points for unlocking and 3.0 points for disarming (base value), it doesn't take more than a few doors and chests to see a skill increase. However, there are a finite amount of locked items floating around, so you need to find a way around that and I have one for you (you just knew I would).
You need four things: lockpicks, a container that can be locked, a "Lock" spell (it's a really cheap Alteration spell that puts a level-5 lock on something for a few seconds) and time. Equip your lockpicks and ready your spell. On your mark...get set...cast "lock", pick the lock, cast "lock", pick the lock, cast "lock", pick the lock, cast "lock", pick the lock... Get it? You'll see both your Alteration and Security skills going up quickly ("Lock" only takes about 1 spell point).