If you are going to work on electrical systems you need to be able to measure things you can't see, and you need to be able to figure out what to measure and what measurements mean. The following link takes you to a good White-Rogers site where,
by clicking on the Installation Instructions link, you can get schematics of water heater circuits and switches.
http://www.white-rodgers.com/common/ptech/appliance/appliance_03.htm#754-1
There are usually three switches in a two-element non-simultaneous water heater thermostat system. Often, two of the switches are combined into one unit. They are:
1. Over-temp switch with manual reset (Double pole, single throw, DPST, White-Rogers 754-1)
2. Upper element switch (Single pole, double throw, SPDT, White-Rogers 756-1)
3. Lower element switch (Single pole, single throw, SPST, White-Rogers 755-1)
The upper element switch and the over-temp switch (1 and 2 in my list) are often combined into one unit (White-Rogers 756-50).
Note that on the White-Rogers site at the link above that the 754-1 and 754-2 models are
incorrectly labeled DSPT; they
should be DPST. The -2 models of the thermostats seem to be for Canadian applications.
Look at the schematics in the installation diagrams. If you can't figure out what they mean then you should probably not be working on your water heater.
You need a decent multi-meter to do any kind of electrical work. There are usable ones for $20 to $40 at Radio Shack or Sears. You need one with at least a 300 Volt AC range and some resistance measuring capability. You probably can't find one that will not meet your requirements for a household meter. If you are seriously into working on things you may want to get one with a clamp-on Ammeter feature, but you probably won't need it. Look at HD if you want that kind.
Turn off the circuit breaker or disconnect the wires of the heater when working on it, but do not disconnect the ground wire, usually green insulated or bare copper.
You usually get the followng types of water heater electrical problems:
1. Heater element burnout, which give you high resistance of the heater element. Resistance, measured across the terminals of the element after you remove at least one wire, should be around 12 Ohms for a 4500 Watt 240 Volt element. If the resistance is much different than that the element is shot or soon will be. Compare with a new element.
2. Heating element short to ground, which means that the resistance between either of the terminals and the body of the heater or ground wire is less than 100,000 Ohms, usually much less.
3. Switch welded closed, often the result of a momentary short circuit when an element fails.
4. Switch always open or always closed, usually the result of a failed sensing element.
5. Temperature sensing error, usually the result of a failed sensing element which may have been caused by a shorted element.
Here is a Bob Vila link for checking out heaters. It is made super-simple but I won't try to rewrite it.
http://www.bobvila.com/FixItClub/Task/Repairing/FIG_ElectricWaterHeater.html