Outdoor outlet on stake in the ground for fish pond pump just stopped working. Pump is okay, Ran extension cord to it. Ground circuit is okay. Checked reset button. How can I find out where problem is?

Do you have power to the outlet? You said you checked ground but what about power from your panel? Is the breaker tripped etc.. If you have power, I would assume its time for a new outlet.

This is a gfi correct?

IF you have a Multi Meter, set it to continuity, place the two leads on the terminals, the meter should beep or show some sign that there is a connection.

If it doesn't there's no connection whether it be at the outlet or in the panel. If there's a connection, go out an buy another plug and just turn off power and swap it out.

Don't do continuity test without verify no voltage on line, or damage to meter may result.
Does GFI Trip and Reset? Verify power in to GFI.

Good Call

Guess he found the problem :D