A model number may help others help you.
Find your model number - AppliancePartsPros.com

Also is it a chest freezer or an upright unit.

The first thing to check would be the control thermostat.
It's contacts should be closed.

Below is my usual blurb on meter usage which may be helpful to you.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.

There is a good STICKY at the start of this forum about it's use.

Another way to check the thermostat is to unplug the unit and the two wires that go to the thermostat's contacts. Then short those wires together, making sure that they cannot short to anything else. Then plug the unit in to see if the compressor starts up.

Also note that there are two types of compressor start devices.
One is a standard relay, the other is a solid state device. The solid state unit cannot be checked easily so usually it is a replace to check it, if the compressor windings check out OK.

Also there is an over heat (clixon) on most compressors.

Below is a good link with general repair info.
How To Fix a Refrigerator - Appliance Repair Guide - ACME HOW TO.com

[COLOR="Blue"] when you say checking continuity you mean checking as well if it is a open circuit vs closed circuit[/COLOR]?
Yes.
Also checking if a compressor winding is ground out ( shorted to the case).
See the link I included.

The thermostat should have two wires going to it.
If the ends plain connectors just pull them off the thermostat and tape them together (short them). Make sure that they cannot short to anything else. Then plug the unit in and see if the compressor starts.

If the connectors are covered is plastic then you could use a paper clip to short the two thermostat connectors together.

Just make sure that the unit is unplugged when working on it.