What is the best legal way to get back money that a coworker owes me?
Assuming that the amount of money that you are owed is not a huge amount, the most likely way to get it back is to bring your dispute to a small claims court. This way, you will be able to (if you win your case) recover your money without having to pay the kinds of fees that it would take to get your money back in other ways.
Small claims courts can be used in disputes over small amounts of money. I have included a link to an FAQ about small claims courts in my home state, Washington, so you can see details about one state's system. In Washington, it costs no more than $29 to file a claim. The claim cannot involve a sum larger than $5,000.
If you are able to document the fact that your coworker actually owes you money, small claims court is the most cost-effective way to recover the money owed.