There is no reliable way to test the capacitor as often they only breakdown when working voltage (120 volts) is applied to them and your meter cannot supply that voltage.

You can check the capacitor to see if it is a dead short or open.
Use a number of different meter scales when doing this.
Also you must short the capacitor leads together between each measurement.
If it is OK at the meter voltage you will see the resistance rise as the capacitor charges.
You may see weird stuff as the capacitor is a non polarized electrolytic.

Here is a link about capacitors probably a lot more than you need or want but I thought I would include is as general info.
http://www.repairfaq.org/sam/captest.htm

You could check the compressor, the below is a good site on how to do this
How To Fix a Refrigerator - Appliance Repair Guide - ACME HOW TO.com
Note: if it checks out OK electrically it may still be the problem due to mechanical problems.