How do you go about tracing an electrical problem that is draining the battery on a Hyundai Elantra?

If you are not comfortable or knowledgeable with the electrical system of a car, have it checked by a mechanic. If the above solution isn't your problem, you can isolate what's drawing the current using this method. You need a multimeter capable of reading AMPS. Remove the ground battery cable and place the multimeter between the battery cable and the battery. Make sure you DON'T run your car like this!! With the car OFF, see how much current is being drawn from the battery. Some current draw is normal, as your cars computer and radio memory functions need power to retain their settings. Start by removing a single fuse and replacing it, each time checking the current on the multimeter. By process of elimination, if you pull the fuse on the circuit that's causing the trouble, the current draw will drop. There's your troubled circuit. Then you'd need a wiring diagram, which you can find on hmaservice.com, and trace down the short circuit.