The two most common ways for a do-it-yourselfer to find a leak is to (1) visually inspect the system for telltale oil stains, or (2) add a can of "leak detector" to the system and then look for the presence of the colored dye around hose connections and fittings.
When refrigerant leaks from the system, it immediately evaporates into thin air leaving no trace except possibly the compressor oil residue that leaks out with it. Wet oily areas around hose connections and fittings and/or greasy streaks radiating outward around the compressor clutch or on the underside of the hood just above the compressor are good visual clues to where the leak is.
Leak detecting dyes will often reveal tiny leaks that might escape visual detection. Some are fluorescent and require illumination with a special light before you can see them. Even so, even dyes can fail to show you where a leak is if the leak is in the evaporator (located inside the heater/defroster plenum under the dash) or in a hard-to-observe or hidden location.
Most professionals use an "electronic" leak detector that reacts to the presence of refrigerant in air. Such detectors are extremely sensitive and can detect leaks as small as 1/4 oz. of refrigerant per year!
Once a leak has been identified and pinpointed, it should be fixed. Don't waste your time on "stop leak" products because they seldom work.
Leaks should be fixed for three reasons. One is because leaks allow air and moisture to enter your A/C system. Moisture can react with refrigerant to form corrosive acids and sludge that can damage the compressor, plug up orifice tubes and/or eat pinholes in evaporators and condensers. Another is because refrigerant is expensive. It may seem cheaper to keep recharging your system with additional refrigerant instead of having the leak fixed, but in the long run it won't be as the cost of R12 refrigerant continues to rise. Third, R12 refrigerant is an ozone-depleting CFC. When it leaks into the atmosphere, it drifts up into the stratosphere and destroys ozone that protects us from the sun's harmful ultraviolet radiation.
Before any attempt is made to repair a leak, any refrigerant that's still in your system should be recovered and recycled. All service facilities that do A/C work are required by law to have such equipment.
Once the old refrigerant has been pumped out of your system, it can be opened for repairs. The desiccant (crystals that absorb moisture and help protect the system against moisture contamination) in the accumulator or receiver/drier should also be replaced if the system has lost all its refrigerant or must be left open for more than a few hours for repairs.
After the leak has been repaired, the system must be connected to a vacuum pump to purge it of all air and moisture before it is recharged with refrigerant. Leaving air and moisture in the system will greatly reduce the cooling efficiency of the system and will lead to the formation of damaging acids and sludge.
It's also important to replace any compressor oil that was lost due to leakage or parts replacement. Use the type and quantity specified by the vehicle manufacturer.
CAUTION: Using the wrong type of compressor oil or too much or too little oil may result in compressor failure.