Remove Hardware. Then Sand Down your dresser. Make sure to wipe the dresser down after sanding.
Prime the dresser with white primer
Paint the dresser with your choice of color. This will probably need several coats (boo!)
After all's dry - and I mean DRY, put hardware back on. You might want to spray paint your hardware which is what I did with mine. Quick, Easy, and Makes a huge impact!
Viola you've got a cute new piece for cheap!