1979 Chevy Caprice fuel

Remove the fuel line at the carb, attach to fuel pressure guage and turn the ignition to the "on" position. For the purpose of confirming the function of the elec fuel pump this can be done without a pressure guage but must be done very carefully.
Remove the fuel line at the carb, place a plastic bottle or jar over the end of the line and have someone turn the ignition on to see if fuel is actually being delivered to the carb. Caution: the fuel pump may be working! This will pump raw gas on to the top of your engine if not done carefully and therefore is not recommended.

If no fuel is present, recheck the electrical supply to the pump and confirm that the pump is actually running.

If you have a carb and the car is a 1979 I do not think you have an electric fuel pump. Your pump is mechanical. After you disconnect the fuel supply line at the carb, you must crank the engine and see if there is fuel going to the carb that way. Make sure you disconnect the battery and the ignition coil wire going to the distributer so there is no chance of the engine starting when you crank it.

Of course, if you don't have an electric fuel pump the original question "How do I check to see if the electric fuel pump and fuel regulator are working properly?" wouldn't have been necessary to begin with. Oh, and by the way, you'll have a hard time doing much of anything with it if you remove the battery.

May be I should have been clearer. You must hand crank the engine by turning the crank with a 5/8 socket a few turns. A mechanical pump will pump fuel with each turn of the camshaft.
Disconnecting the battery is a saftey precaution. If you leave it connected and crank the engine with the starter -- with the fuel supply line disconnected at the carb -- and there is nothing wrong with the pump -- then you will spray gas all over the engine compartment. The rest could potentialy be catistrophic.