The air conditioning just blows warm air. The a/c was working at one point, but it began alternating with the hot air a few months ago. It would blow cold air just fine, but as soon as I stopped somewhere and after say an hr I got back in the car the a/c would blow hot air again. This happened consistently until recently when the a/c stopped blowing cold air all together. It doesn't matter how long I leave it on for, or how low I put the cold setting, it still blows warm air. I took it to the dealer and they said it would cost $250 just to look at the car, which blows my mind, but also leaves me curious. Is it because the problem itself is a cheap fix, and is a common one in 2002 Hona Civics? Does anyone have any suggestions of what it might be, or what I can do on my own to pinpoint the problem?

$250.00 just for diagnosis?

I'd get that statement in writing and contact the Honda dealer representative.

That figure sounds more like the diag and repair.

Shop around. There are qualified shops that will charge little or no diag fee, because they're hoping you'll buy the repair(s). Ask about diag fees upfront and also about tech credentials and warranties. If they don't want to be open DON'T give them your keys.

You'll need to take your car to a qualified mechanic to diagnose the failure.
Your A/C system most likely has a leak.