Pick-Pocketing.
Pick-Pocketing is the first thing you most learn when it comes to the Thieving Skill. You'll be able to pick-pocket a man by simply right clicking him and clicking Pick-Pocket. There is a slight chance that you get caught, which in turn will make the person attack you as shown in the picture besides the text. Here is the Level tables for Pick-Pocketing.

Level Tables for Pick-Pocketing
Character Level Exp. Gained
Man lvl 1 8 Exp
Farmer lvl 10 14.5 Exp
Warrior lvl 25 26 Exp
Guard lvl 40 46.5 Exp
Knight lvl 55 84.25 Exp
Paladin lvl 70 151.75 Exp
Hero lvl 80 273.5 Exp

Stall Stealing
You can occasionally find a stall to steal from. Like pick-pocketing though, there is a chance that a local Guard or Stall Owner can catch you and attack you. To steal from a stall, right-click on it and click "Steal". Here are the level tables for stalls.

Level Tables for Pick-Pocketing
Stall Level Exp. Gained
Baker's lvl 5 16 Exp
Silk lvl 20 24 Exp
Fur lvl 35 36 Exp
Silver lvl 50 54 Exp
Spices lvl 65 81 Exp
Gems lvl 75 16 Exp

Lock-Picking
With a good thieving experience, you can open locked doors by picking their locks. To pick a lock, right-click on the door and click "Pick lock". If you succeed, you will walk through the door as you have opened the lock. However, the next time you wish to go through the same door, you will have to pick the lock again.

A lock pick may also assist you in picking locks. Lock picks are obtainable by pick pocketing Rouges that are found in the Wilderness.

Disarming Traps
Traps are usually found on staircases, levers, and chests. To disarm them, you will need to right-click and then select, "search for traps". If there is a trap that you have discovered, it will be automatically disabled if your thieving level permits.