Inspect the hoses leading into the pump to look for signs of cracking, corrosion or leaking. Shut off the pump and replace any hoses that are damaged.
Look at the pump housing to search for cracks. Clean cracks off with a damp cloth and dry them with a rag. Seal cracks with epoxy to prevent water leaks. Severe cracks likely require a full pump replacement.
Open and close the valves on the pump to make sure they move smoothly. Apply lubrication to any valves that are tense to help prevent the valves from sticking.
Sand any corrosion or rust off of the pump with fine sandpaper to prevent it from getting worse and from locking up the pump.
Listen to the motor on the pump. If it is sputtering or not running properly, it likely needs replacing.
Tap the pressure switch with the handle of a screwdriver. If this causes the pump to turn on or shut off, replace the valve with one of an equal pressure rating. Turn the pump off and label each wire going to the pump using tape so you don't get confused reattaching them. Unscrew the conduit locking ring first and then unhook the wires. Unscrew the old switch and nipple by twisting it off and twist a new one back on. Unscrew the pressure gauge with a wrench and screw a new one back in. Reassemble the wiring and the locking ring.
Request professional service for the pump if it still doesn't function properly.