It isn't necessary to remove the elements or drain the tank to test them, but the elements must be removed (and the tank drained) to replace them. To test the elements, you will need a voltage/OHM meter. Turn off the power to the heater first and disconnect the two wires to the elements. Set the meter to the "OHM" function, and check the flow between the two screw connectors of the elements: If there is a positive reading, then the circuit is "closed" and the element is fine; if there is no reading, the circuit is "open" and a new element is needed. Also, if you get a reading on your meter between either of the screw connections and the metal element, the element is shorted and must be replaced. You should expect an approximation of the following readings on the OHM meter (give or take a little) for functioning elements:
