We have solar panels on both our fifth wheel and our slide-in truck camper: 4 on the fifth wheel, 2 on the camper.
The solar panels will not *run* your refrigerator...the sole purpose of solar panels is to charge batteries. In order to use the batteries to run AC appliances, you will need a properly sized inverter.
However, I would not recommend trying to run a refrigerator on AC using an inverter...it would quickly drain your batteries. When dry camping, run your refrigerator on propane.
What size do you need? That depends entirely on how much roof surface you have and what you want to run. Here are a couple of solar educational pages to help you determine your needs:
1)
http://www.amsolar.com/education.html2)
http://www.rvsolarelectric.com/The second site, in particular, has a LOT of good information, including a worksheet you can use to help you figure out how much power you need. Of course, you'll need to strike a happy balance between the room you have to install everything, the price you want to pay for all of it, and the stuff you want to run.