Find an area of the dresser that you can sand, to get a little sawdust. If the scratch is large, mix the sawdust with some white glue (woodglue), if it's small enough, mix with Cyanoacrylate glue (super glue), which will cure clear. Fill the scratch and when dry, sand. It won't be perfect. You could also consider sanding down the whole surface, if the scratch is VERY shallow.
You can buy a set of waxes from a kitchen shop, they come in various colours. You simply rub the wax over the mark applying pressure, do this until you think the scratch is filled andthen simply polish the residue away with a cloth and some elbow grease. Thats the proper way to do it, i always carry a set of waxes in my van just in case.
Don't use glue and sawwdust or you will wreck it.