Depends on the kid - some do very young, some aren't all that interested. My son isn't born yet, but my daughter (2.5) has on a couple of occasions. I've just told her that it's okay to touch herself, but it's a private thing to do. She needs to go to her bedroom if she wants to (cue running to her room, and coming back 30 seconds later when she's found something more interesting). Also I mention that she then needs to wash her hands.
I know another little girl who was very hands-on from about 1 to 4. Don't know whether she kept it up as she's old enough to understand privacy now :P