To steal an item when there are a lot of people around, get it in your crosshairs and the pick it up. Then, walk to an area without any people, drop it, and steal it. For example, use the Bottle Cap Mine in the Craterside Supply on the work bench, pick it up, then drop it at the end of the desk to the right, next to the two metal boxes. Enter Sneak mode, get next to the desk once your indicator says hidden, and steal it.
To steal items without getting caught, get in Crouch mode when the "hidden" description is displayed on the screen. Some heavily guarded items require a high Sneak skill; use the "Grab" ability to steal those items. Then, move to a darker part of the room until "detected" changes to "hidden".