I work on these things all the time. . Electrics are the easiest to troubleshoot, and the cheapest to fix.
First, you need an amp-probe. Turn off the power, and take off the upper and lower covers. Check your elements for sizing, theyre prolly 240volt 4500watt (most common) 208v is possible also. At 240/4500 you should have approx 18. 75 amps. 208/4500 is 16. 25. Check your voltage first before amping them. Bend out one of the wires on each element with the power off so its easy to clamp them. Always be very careful around high voltage.
If your amp readings look ok, you may have one of the other faults, a bad thermostat (usually doesnt cause a breaker to trip), or a weak breaker. With the power off, you can check the operation of the thermostat. Here is a link to a typical wiring diagram.
http://www.hotwaterproducts.com/BWC/Parts/Pdfs/Electric Wiring.pdf
use the first diagram on the left.
On a cold tank, the upper stat calls first, providing power from terminal#1 to #2. #3 to #4(upper) are unswitched. When the upper stat is satisfied, it switches power from #1 to #4(lower). Then the lower thermostat heats the rest of the cold in the tank.
Its possible you have a sticking thermostat which may provide power to both elements at the same time. Doesnt happen very often, but if it isnt a weak breaker, you can change out all the parts behind the access panels for 50-60 or less. If your tank is more than 3-4 years old, you should prolly change out the elements anyways. If the tank is still under warranty, its worth it to call it in. This is the majority of my work. (warranty stuff)
any other q's, pm me and i`ll help ya out. .
-jerry