The visible part of the external power receptacle consists of a small hinged door concealing a socket with one or more metal pins. The pins receive a large plug at the end of wires attached to a portable battery cart. When plugged into the receptacle socket, the cart supplies battery power to start the engine.
If you find yourself with a low battery, but the airplane has an external power receptacle (typically it is an optional, extra-price item on a new aircraft, so not all airplanes are equipped with one), and the FBO has a functioning battery cart, chances are good that you will be able to get the engine started and be on your way without too much delay. If the airplane does not have an external power receptacle, you're probably looking at removing the battery to have it recharged.
Consult the airplane flight manual or pilot's operating handbook for specific procedures to follow when using a battery cart and external power receptacle. In most cases you'll need to ensure that the master and alternator switches and all electrical equipment in the aircraft are off before the line technician plugs the battery cart into the external receptacle. This is to protect the aircraft electrical system from voltage spikes.
Once the engine has started, let the technician remove the plug, then flip the battery master and alternator switches to the On position. Check the ammeter and any electrical system annunciators to ensure that the electrical system is operating properly and the airplane battery is being recharged (as indicated by a higher-than-normal reading on the ammeter needle for a few minutes after engine start). When the ammeter returns to its customary position, the battery should be charged and you should be good to go.
The most important thing to keep in mind when using the external power receptacle is to proceed cautiously, especially if the receptacle is on the nose of the airplane. In that case, the line technician will have to reach in behind the spinning propeller to pull the plug from the socket.
An external power receptacle is a handy feature when it's needed, but above all, when using one, be safe.