Turn off the electrical circuit that controls the fountain and drain the water from the fountain.
Disconnect the rubber tubing from the pump head. In most cases, the tubing simply pulls off the pump head but in other cases, you must loosen a band clamp with a Phillips or flat-head screwdriver before you can pull the tubing off the pump head. If you have trouble locating the pump, trace the electrical cord for the pump from the outlet to where it goes into the fountain. The pump is usually black and relatively square.
Secure the air hose from your air compressor to the end of the tubing with duct tape. This creates a seal between the air hose and the water tubing.
Apply 15 to 30 pounds per square inch of air to the air hose. As a caution, do not stand in front of or allow anyone else to stand in front of the area where the water comes out of the fountain just in case the clog is solid.
Increase the airflow until the air flows unrestricted through the water tubing.
Turn off the air compressor and remove the duct tape from the tubing. Reattach the tubing to the water pump and fill the fountain with water.