I work for a property office and I have a few people that I need to garnish their wages but I am not sure of where they work. How would I find out where someone is employed using their social security numbers and their names?

What do you mean by "property office"? Is this some sort of government agency?

In general, before you can garnish wages you will have to get a judgment against the debtor. To do that you will probably have to serve them with process.

I have a feeling it's a landlord's management office.