I want to test an electrolytic capacitor in an old guitar tube amp.
An ohm meter can be use to determine if a capacitor should be functional. A meter with meter works best or a DMM with a bar display. A short is obvious, and if the meter needle doest show that the meter's battery isn't charging the capacitor is open. In tech school that had us construct a circuit using a Wheatstone http://en.wikipedia.org/wiki/Wheatstone_bridge that allowed one to determine the value of an unknown capacitor or resister. Unfortunately I lost track of my note books, so I can't provide further detail. But I believe this may be what you are looking for http://www.ecelab.com/wien-bridge.htm
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Of course capacitors die often... sure signs are leaking fluids, bulging, and heat damage. I'm assuming that if it was painfully obvious, there would be no need to ask the question! Sometimes capacitors die quietly, and physically look fine. The only reliable way to know for sure is to test if they have the correct capacitance.
Remove the capacitor from the board, and feed it a small square or sine wave from an astable 555 timer or other device.
Compare the input and output voltages. A capacitor will exhibit impedance to this sort of signal in a similar way to how a resistor resists DC. You can then roughly calculate the capacitance of the capacitor... if it is way off, time to replace it.
Alternatively, make a schmidt-trigger NOT gate oscillate using that capacitor and a resistor. The frequency of the square wave output can be used to calculate capacitance.
A less reliable way would be an LED and a resistor. Charge the cap, time how long it lights up the LED. Knowing the voltage drop across the LED, the power consumption of the LED and the resistor, as well as the starting voltage, you can again estimate capacitance with some large (but perhaps acceptable) error margin.
You could also just replace it for the same cost of building any of those test circuits (cheap). Remember to observe polarity, and choose a unit with at least as high a voltage rating as the piece you are replacing (higher if possible).
basically what gmoon said is right but here are some ways to detect obviously bad capacitors
is it deformed or shows signs of overheating ?
if you connect it and a led in series to battery does the led shut down after some time ? if it keeps lit all the time the capacitor is bad
is the capacitor more than 20 years old ? thats about the max life of electrolytic capacitor (way shorter if it has hard life)
You could build your own...there are several types. Some use analog meters and some use frequency counters or microcontrollers.But I suggest you search ebay for "capacitance tester" -- bought a VOM with cap and inductance testing capabilities for < $25 USD.