When fixing my '82 a/c, where do I start? I believe the compressor is okay. Should I first use a dye to check for leaks?

First you need to do lots of learning.
Go to Aircondition.com and read and read.
Got to the library and see if they have a text from a trade school on Air Conditioning... study the basic theory and then study the Automobile AC section.
Pay particular attention to the SAFETY WARNINGS....
35 years ago, by not studying first, I almost blew up a can of R12 in my face. I had hooked it up to the wrong side and it was already getting HOT when I accidentally felt of it...
There are also books just about Auto Ac... check out Ebay, that is where I got one of my books...
Then start trying to find the stand alone Mercedes Factory Shop manual which addresses the Climate Control System. It is a great book.
Do a search on this site using either Larry Bible or Leathermang as the posters.. that will bring up lots of AC Wars with great information.
Then post more specific questions about your car and we will be able to help--Greg