You should be able to head to sears or best buy or somewhere and pick up a new 3-prong plug. I woulndt recommend replacing the outlet on the wall. This outlet is 240V, and while in theory that should be no different than any regular outlet, I wouldnt risk it if this is your first time. (Open the breaker at a MINIMUM), but I'd let a professional deal with 240 if I were you.
But...you can replace the lead and plug attached to the dryer fairly easily. There should be a cover you can take off, a couple wirenuts to undo, purchase a new lead with a 3-pronged plug, re-attach to the dryer using NEW wire nuts (probably come with the plug). Put the protective cover back on, slide the dryer in place, line up the ventwork, plug it in, test it, and you should be good to go. Don't mess with the wall outlet. Should cost you about 20 bucks.
Edit...oops 240 not 440...