It could be the matter of replacing a small part or the whole air conditioning system. Even if you want to do the job for yourself, this leak finding service should be the one thing that you should get the professionals to do. It could save you a lot of money and will save you a lot of time for not much expense.
The most common problem is, after all, a hole in the condsener. If you live in a part of the country where they regularly salt the roads during the winter months, there's a chance a big chunk of grit could have got flung in to the system and created the hole. The leak test will tell you if that's where the problem lies and the garage will also recommend whether you need to replace it or recharge it.
The low side port for the air condititoning system is located on the compressor. It is below the intake manifold on the driver's site. The high side port can be found near the steering pump at the edge of the driver's side engine compartment. If your care dates back to before 1994 you will have the old R12 refrigerant system which has now been outlawed in the USA making it near impossible to find a direct replacement. Therefore a simple small part replacement is what you are going to have to hope for with this job.
If you do need to replace the system though, you can get a conversion kit to allow your old system to use the new R-134a fittings.