how are they used

There is a single throw thermostat for the lower element. When the water temperature down there drops far enough the switch goes to the on position.

There is a double throw thermostat for the upper element. As long as the water is hot enough this switch is set to send power to the lower thermostat when needed. When the water up top gets cool the upper element is switched on and also the lower element is overridden. This is because the water heater only has one element on at a time so as not to draw too much current.

If the lower element fails then the upper element will continue to operate but only the water in the upper part of the tank will get heated after which time the upper thermostat switches to the lower element that now does nothing.

If the upper element fails and later its thermostat switches to upper element then the water heater can get stalemated with no heating. It won't switch back to the lower element until the upper half of the tank has been heated which won't happen with the failed upper element. If you don't use enough water at one sitting to activate the upper element then the lower element will keep cycling on and off normally.

If the upper thermostat should get stuck in the lower element switch position then the heater continues to heat the entire tankful but after a big draw it takes longer before the water as drawn from the faucet gets hot. While gas water heaters heat only from the bottom, gas heaters heat a lot faster than comparable grade (standard versus heavy duty) electric heaters even with no defects in either.

(There are a small number of heavy duty water heaters that will have both elements on at the same time but these are not the models sold in ordinary stores like Home Depot.)