Good bunters describe it as catching the ball with the bat. But most hitters don't get it—the bat doesn't look like a mitt, etc. It's another of those easier-said-than-done situations—unless you can do it well, in which case it's easier to do it than explain it.
Two reasons that most batters can't bunt well is that they're taught sixteen different ways of doing it by guys who never did it well themselves. And, they think too much in the act. The ones who do it well bunt with their eyes, their hands and feet merely squaring to their vision. It's more controlled than swinging away, but no less active; squaring to bunt, the batter reads the pitch in a different way, from a different angle—usually from a lower crouch, facing the pitcher and pitch head-on. To the extent he can do that, reading the pitch and letting relaxed hands and bat triangulate the best angle, a hitter can indeed catch the ball with the bat head, soaking up all the pitch's energy with a soft thud and dribbling the ball down away from the plate, away from the catcher and into the zone that forces defenders in toward the batter and away from the bases.
Good bunters bunt strikes. It's never a good idea to bunt at balls out of the strikezone, because you're just making your job harder and the pitcher's easier.
A smart baserunner at first knows that the bunt sign means to run when the ball's bunted, not when it's pitched. It's not a straight steal. He can get a better secondary lead if the first baseman charges, of course—but even if he's held on, a decent secondary and a decent bunt will get him safely to second.
If the bunt is a suicide squeeze, the runner's coming down the line and the batter's bunting the ball wherever it's pitched. He either makes contact or that runner's a goner. Such situations define the very best bunters, whose relaxed bat-on-ball transfers all of the pressure back onto the defense. It's the easiest rbi in baseball, and one of the rarest.