being able to work on a car and being able to work on A/C are two completely different animals.
Honestly, there may be nothing wrong with your car aside from being low on refrigerant. While the o-rings that seal the lines sometimes go bad, the answer may even be more simple than that. Modern cars use R-134A. This type of refrigerant is better for the environment than older R-12, but it comes with it's own set of problems. R-134A has a smaller molecular structure, so it is more likely to leak out than R-12, especially during the winter when parts get cold and shrink, such as o-rings. If your car sits a lot, then your A/C wont run at all during the winter, and I cant remember off the top of my head whether a 95 contour will run the A/C while you run the defroster. Newer cars run A/C while running the defroster to help reduce humidity, also circulating the refrigerant helps lubricate the parts since there is oil in the refrigerant. Now, like I was saying before, R-134A leaking out past seals and o-rings, even in a well maintained or new system is very common, even on a car with everything working properly, it doesnt hurt to charge your A/C every few years.
But I do have to go back to another point. You can buy a kit from the parts store to help charge your A/C or at least test it, but generally if your system is low enough that it wont turn on the compressor, you wont be able to charge it with one of those kits. You will want to draw a vacuum on the system so that you can get the air out and get the refrigerant in.
Please understand that noone is questioning your mechanical ability, just A/C systems are very different from working on engine parts. They are also not something you could usually diagnose without knowing a lot about how A/C systems work. I have been working on cars for a lot of years, and do know a bit about A/C but honestly, I would still leave a lot of stuff to my dad when it comes to that, cause he specializes in heating and refridgeration. Its always better to take that kind of thing to a professional, I hate to tell you to spend a bunch of money, but if you dont know A/C systems, you shouldnt mess around with them, because they are not a user servicable part. There are reasons why A/C shops have the manifold sets, the reclaimers, vacuum pumps, gauges, and other things, there are also reasons why guys who do A/C have their own set of certifications and training courses.