A wide array of problems in guitar pedals can be traced back to dirty components. Getting to the pedal's inner workings is usually no more difficult then removing a set of screws and opening the housing, but make sure the pedal is not connected to an electrical outlet or amplifier before you get to work. Do not use water or any chemical solvents, as these can permanently damage delicate electronic components. A compressed air cleaner is the best tool for this job. Use it to carefully blow away all dirt and debris from inside the housing, making sure not to damage the circuit board.
Issues with the power supply are common and generally easy to deal with. Usually a battery that is low or dead is to blame, so test the battery with a voltmeter to make sure there is sufficient voltage. Most effect pedals take 9-volt batteries and need at least 7 volts to achieve maximum performance. Test the battery both in and out of the pedal. If there is a sufficient charge and the pedal still doesn't work, check the wires that connect to the battery terminals.
More often than not, damaged wiring is the cause of a nonfunctional effect pedal. Check all wires inside the housing for cracks and fraying, keeping an eye out for breaks in the insulation, as this is the most common source of damaged wires. Remove any broken wires with a toothpick and solder in new ones. Take extra care not to let any plastic insulation melt and drip onto other components when re-soldering wires. For older effect pedals, replacing all the wiring at once will ensure that less frequent repairs will have to be made. Many other problems can be easily solved with some quick soldering. Check all the joints on the circuit board and repair any broken connections.