When you do something ineptly, you really bungle it, or mess it up. A play that's ineptly directed and acted is painful to watch.
A waiter who does his job ineptly is likely to bring you food that someone else ordered and to spill water in your lap when he's refilling your glass. The adverb ineptly implies doing something not only badly, but in a clumsy or awkward way. The Latin root of ineptly and its adjective form, inept, is ineptus, "unsuitable, awkward, or absurd." It comes from in, or "the opposite of" and aptus, "fit or suited."