Bring your painted dresser to a place where you'll have a lot of room and good ventilation. Put it on a drop cloth. Take out the drawers.
Hit it with something heavy that can damage the finish, such as metal chains. You can use a hammer a few times as well, but hammers will leave identical circle marks, so don't overdo it, or it will look unnatural.
Hit the drawers. Make some nicks along the edges of the drawers as well as on the front surface. Take out your frustrations on it -- the results will be bolder.
Grab a putty knife, a screwdriver or some other sharp object, and gouge the wood in a few places.
Tap a nail into the top 1/4 inch of the wood with a hammer. Make a small cluster of these with different sized nails to look like worm holes. Do a few on the drawers as well.
Sand down the painted dresser with a fine-grit sandpaper all over, just to dull it. Upgrade to a coarser sandpaper, and sand vigorously along edges, on handles and corners to wear off some of the paint and expose unfinished wood.
Rub some dark brown or black shoe polish to some random surfaces or edges to discolor it. Use a very light coat on a rag. Rub it in well, then wipe off excess. Stop when you're satisfied with the look.