No Hot Water
Check that the unit has power. If it has power, then press the red button to reset the heater. Check the thermostats to make sure they are both set at the same temperature, but no more than 120 degrees F. If there is still no hot water, the upper thermostat is probably defective and you will need to replace it.
Not Enough Hot Water
Check that the thermostats are set high enough and that both are set to the same temperature. If it's wintertime, the cause could be a lack of insulation around the tank and the hot water pipe--insulate the pipes and heater properly. Sediment buildup in the tank will also affect the amount of hot water available, so remember to turn off the power, drain the tank and flush it out every six months. The tank may also be too small for your family's needs--if this is the case, you will need to replace the heater with a larger model.
If the tank doesn't refill with hot water fast enough, the problem is probably either the upper or lower heating element--you will need a multimeter to check them. Both elements are checked in the same manner. First, turn off the power at the service panel and check for current on the heater. Open the access panel and remove one of the wires from the element. Set your multimeter to 1000x and touch one probe to the element mounting and with the other touch each terminal screw. If you get any reading at all, the element is bad. Then set the multimeter to 1x and hold each probe to a terminal screw. If you don't get a reading here, the element is bad.
Leaking Relief Valve
The relief valve will drip due to excessive water pressure or a closed system. Do not plug this valve. To stop the dripping you can either install an expansion tank or a pressure relief valve on the cold water supply line.