If I had the game I'd tell you, but isn't that information found somewhere in the manual? Also, considering that games these days seem to disable some features until the game decides to teach them to you, it may be possible that you can't actually sneak until the game decides you need to know how to and tells you. As I said, I haven't played the game, so I have no idea how the tutorial is set up (assuming there is one). Hope I've been of some help though.
click the thumbstick, odd thing but the game won't let you enter sneak mode until you leave Doc Mitchells
Left thumbstick, click it down once. Click it again to stand. Your sneak, or your ability to sneak should I say will depend heavily on your skill level. This also effects your ability to reverse pickpocket grenades into your foe's pocket. There's also a perk that will allow you to run while you sneak that negates the run factor called Silent Running. I always take it, though I usually wait a while before I take it. It will take at least a fifty in sneak to get certian weapons into the casinos though if you play your cards right you can carry all of them into The Tops almost immediately. As of late in my runthroughs I don't run my sneak up over fifty, then add whatever books I find. I prefer to use the extra points elsewhere and from what I gather it won't make much difference to run it up to 100 sooooo..... (It will show you how when you go out to the wells with whatshername in Goodsprings to shoot geckos if you let her take you with. You'll also get a varmit rifle and some extra ammo if you play along with her.)