turn off the power.
Disconnect the wires from the element.
Use a continuity tester. The setting that beeps when you touch the 2 test leads together.
Test each terminal separately.
one test lead on element terminal and the other lead to tank.
test the other element terminal the same way. one to terminal and the other to tank.
If it beeps then the element is burned out.
If you test both terminals with one test lead to each terminal you should get a beep. This only means you have continuity.
You need a
amp meter to properly test an element to see if it is working.
with all the wires reconnected and power turned back on.
If the heater is cold the upper thermostat should be calling for heat.
you should have 220-240 volts with a Volt meter test leads
One on one element terminal and the other test lead on the other element terminal.
Before you do that check voltage at top terminals where the incoming power supply is connected to thermostat.
touching both terminal with a test lead to each one should be 220 to 240
volts.
not all thermostats are wired the same.
upper stat comes on and heats upper half of tank.
when that upper stat is satisfied it switches power to lower stat.
then the lower element will heat until that stat is satisfied, and then shuts off.
The lower stat does most of the work once the tank is hot.
cold water coming in kicks the lower one on first because the hot water rises to the top.
There are plenty of
how -to test electric water heaters info already out ther on the net. should be easy to find