Replacing the capacitor in a window air conditioner is no a difficult task but car must taken so no harm is done to yourself or the unit.
If you have no experience in HVAC, electrical, or other equivalent background it would be best to buy a new unit since high voltage is fed into the capacitor.
Most all air conditioning systems use large capacitors to help the compressor start and the condensing fan motor.
There are different engineering solutions in some cases but most will use a capacitor to either help start a component or help it run evenly with no high or low spikes.
Most units will use a Dual Round capacitor that is two capacitors in one package. This is done to save on space as two separate capacitors would take up more space.
Symptoms of a bad capacitor include the compressor not starting or the condensing fan not coming on.
The capacitor needs to be tested using a multi-meter that is cable of reading micro-farads.
Before testing or working with the capacitor be sure the unit is unplugged and discharge it as it can still hold a charge that can give a shock even while not plugged in.
Discharging the capacitor is done by grounding a leg of a wire and touching each leg of the Cap for 3-5 seconds making sure it is drained of any charge.
If you have no experience draining a capacitor call a professional.
Once the unit has been unplugged and capacitor no longer has a charge it can be removed to see what micro-farads it is rated to use.
The Cap will give its value in Micro-Farads. Dual Rounds give two values such as 35uF and 5uF. The higher value will always be for the compressor while the lower value for the fan.
Before testing it or replacing the CAP be sure to label the wires and take pictures so the correct leads go back to the correct legs.
Most Dual Round Caps have a “H” for the compressor, “C” for common, and “F” for fan, again these can vary from manufacture.
A multi meter capable of reading the capacitors values must be used to get accurate measurement. These types of meters are used by HVAC and electricians technicians.
Read here for more on HVAC capacitors testing and replacement.
Once a capacitor is found to be bad it must be replaced. The values on the capacitor including micro farads and voltage must match the one being replaced.