What is my first step diagnosing my leaky rear tires on my John Deere 2020?

This tractor has been kept inside for several years, sitting on concrete in a shed, but recently the rear tires have begun deflating. To admit my ignorance, I have never known anything about the process of how tires are filled with water. The tires themselves are in very good condition (less than 10 years old) but I am afraid the rims are corroded and rusting through. If the rims are shot, are they hard to find? The tractor runs fine if I need to load it up. I do not have the proper jacks, tools or know-how to do much myself. I was just wondering where to begin. I'm sure a mobile tire service would cost a fortune and I don't even know what he could do for me. The tires say "Multi Trac L/S Rear Tractor" R-1 14.9 - 28 on 13" rim.
Any advice would be helpful.

Burt
February 2012