I have three outlets in my basement that show they are hot using a simple tester. However, when I plug anything in they do not work.
Any ideas on what steps I should follow to get the circuit working?
What is this "simple tester"? If you are using a proximity (induction) tester and are getting a "hot" reading, then I would suspect a loose neutral wire. Look at the closest receptacle on that circuit that is still working. You may have a loose white wire, probably loose because the push-in connection was used. Repair using the screw terminals.