How do I diagnose and fix an electric water heater leak?
Good question. If the threaded insert points where the pipes themselves are attached to the unit are not leaking or if the pressure relief valve threads are not leaking then it may very well be the tank itself that is leaking.

To check the threaded connections you will have to dry out the areas of the "wells" and around the pressure relief valve. Once dry then check the threaded areas for leakage. A dry paper napkin be handy to check for wetness around the pipe connections. If you find pipe thread leaks it will be necessary to disassemble the plumbing and then clean the threads and reassemble with good quality TFE pipe thread tape in the joints. 

It is possible that the pressure relief valve itself is leaking out the blow off exit opening. Normally this should have an overflow tube attached to it that aims toward a floor drain or through a wall to the outside. If this was never installed on your heater then the leak could be dribbling out of the exit pipe connection and running down into the top of the heater unit. If you find water leaks from this the pressure relief valve is replaceable.

If the investigation of the above items does not turn up anything then it is most likely a tank leak. Such leak invariably leads to a heater unit replacement. If tank corrosion has lead to a leak in one place there is highly likely to be other areas of the take with leaks waiting to happen. For this reason, even if you could determine a workable patch for one tank pinhole, it is recommended to somply replace the tank.

Use care around the tank if the insulation is dripping wet. If this has gotten into the electrical controls or connection area there is a possibility of electrical shock. Do shut off the electricity at the panel before doing any work for safety sake.