Here are your parts includes a wiring diagram.
Replacement parts for FRIGIDAIRE FRS22ZRGD0 Frg(v1) / Refrigerator | AppliancePartsPros.com

First you have to find out if the compressor is running.
You usually can hear it also you should be able to feel it vibrating and it should be warm.
If it is running, I would remove the cover inside the freezer so you can inspect the coils. It there is no frost or just frost in one area then you have a sealed system problem. Note that this test must be done after the unit has run for a couple ours, if you do this just after a defrost cycle then there will not be any frost on the coils.
A sealed system problem will be an expensive repair as you will need a pro. Usually it makes more sense to invest those dollars into a new unit.

If the compressor is not running you have to check if it is getting power.
If there is power then it could be a bad start device or a bad compressor.
If there is no power then it could be a bad control thermostat or defrost timer.

Here is a good site with info on how to check things
Appliance Repair Guide: How To Fix a Refrigerator - ACME HOW TO.com

Also here is another site with basic fridge repair info.
http://www.applianceaid.com/frig.html