Hello and welcome to oDesk. I do not work for oDesk but I have experience as both a contractor and client. I'm certain that moderator Valeria's advice and suggested reading will be all that you need, but just in case a few unusual things may have happened, let me offer the following tips...
Sometimes a very new contractor may do fixed price project work and be unaware that they need to submit the work using a button on their side of the oDesk interface. If they did not do that, up you can still pay them, but it is trickier. So if they are new, ask the to look for that submit milestone button and have them use it. That puts a request for funds in front of you.
Also, if you have a VERY new contractor, they might not have known how to log time using the time tracker application called Team. If that happened, you can ask the, to submit their hours manually, or you can pay them in the form of a bonus. But ask them to learn how to use the time tracker properly, because you only allowing them this concession once.
Finally, if both you and the contractor are so new to oDesk that neither of you knew how to properly set up a contract before the work was done, do not panic or be embarrassed. This happens a lot. You can still create a fixed rate contract to pay for the work or you can ask customer support to help you. Just be sure to pay the contractor only via oDesk, not matter how much help you need to ask for, and everything should be fine. ODesk IS complicated and tricky to use the first time, but it gets easier fast and most of us here don't even remember that when we started out we didn't really know what we were doing either.