Stealing is a tricky business and any failed attempt will prompt the player to "load game" unless they want to have a whole town run them through. Stealing, however is the quickest and easiest way to gain experience and level up, especially in the early stages of the game.
There is a safe way to pickpocket NPCs, without having the mob cry out for blood every time you fail. You can achieve this through the help from one of your NPC team mates. The first NPC you can recruit (if you choose to do so) is Ian, a wounded mercenary resting in Shady Sands (located between vault 13 and 15).
When you successfully recruit him (and thus, gaining 100 experience), remove him from the party and start stealing items from him. If you know already, stealing in sequences without exiting will provide more experience than just stealing one item and exiting: 1 sequence = 10 exp, 2 sequence = 30 exp, 4 sequence = 100 exp, and so on.
Failing to steal (pickpocket) from Ian will not alarm the other NPC's and thus, they will not attack you, nor will your reputation (karma) be harmed. If Ian runs out of items to steal, simply place items back in his inventory (planting items), and repeat the process. Note that planting items also gain stealing experience.
Also note that stealing from Ian (or other NPC in your team) while he is still active in your team, will not bring you any experience points, so remember to remove him from the team, as you can always recruit them later. This process is also useful for equipping your comrades with weapons, ammunition and other items, as there is no way to easily equip them from the "barter screen".