Make sure you turn the power off to the water heater before conducting the following test.
Check the elements with a continuity tester with both wires off the element. You should have continuity when probing to each screw at once. If not the element is faulty. If that tests out "ok" remove one probe of the meter and touch it to the bare metal tank. You should not get continuity. Do the same for the second screw terminal on the element. You should not get continuity. If you do the element is faulty.
Do that for the upper and lower elements.
Check the high limit reset. Its the red button near the top of the upper thermostat inside the top access cover.
Make sure the power is off before starting.
Make sure the thermostats are held tight against the tank. Make sure all your wire connections and screw terminals are tight. Inspect the wiring in general.
This is no means a complete guide....but its a start for you.