To actually repair an AC system you need at the very minimum a vacuum pump and gage set. Amateur or not, the tools you have limit what you can do. For finding a big leak Freon with dye and single fill line hose will do. Smaller leaks and you need to add a UV light to see the UV dye. For really small leaks you need to add a sniffer and even though you can get all these things from harbor freight, there is a point where having this done cost less than doing it yourself.
Adding Freon with dye and finding a big leak is about a 15 minute job, put it in, let it sit overnight, look for the green puddle in the morning and follow the trail back to the leak. If you find your big Freon leak is the line set seal, replacing the seals and having the system charged at a shop with all the tools cost less than buying everything you need to do the job once. A few dollars for Freon with dye could keep you from getting stiffed for a compressor replacement you don't need and any leak you find that you can fix yourself can save you hundreds over the cost of having someone else do this for you.
So someone told you that you need a new compressor and you don't find a big leak at the line seal, odds are the compressor is leaking internally between the high and low side. An amateur mechanic can replace the compressor and install new seals. For less than the price of the cheapest set of tools to do the rest of the job, you can have the system vacuum checked and charged. Don't know what this cost in Oakland, where I am you can install two good used compressors that aren't any good and still come out ahead.