Unless you paid extra for Microsoft Office (Word, Excel, ...), you already have a free trial copy. It will be good for 25 uses (of all Office programs combined) or 60 days. Until then, you don't need a product key for it. Just click the Continue button in the registration window without entering anything in the product key boxes.
But be warned: When the trial period expires -- with little or no warning -- you'll be able to read and print your documents, but not much more. When that happens, here are some of your options for paying less than full price for Microsoft Office 2010:
First, since you'll be a student, you may qualify for the Office Professional Academic edition of Office at a pretty good price ($79.95):
http://www.microsoft.com/student/
Second, if you’re interested in buying just Word, check out this URL, especially the second group of listings.
http://office.microsoft.com/en-us/products/FX101754511033.aspx
Note that the higher of the two prices quoted is for a full version of that program and the lower, for upgrades from existing software. Read the list of upgrade-qualifying software carefully: MS Works is often one, and may have come on your machine.
Finally, if you're willing to spend a little to save a little, Microsoft Works is available in stores for about $40.00. You could buy a copy, install it, then buy Office at the upgrade level. I think you'd come out ahead. Note that the upgrade copy probably checks your machine for Works' presence, so don't get rid of it after you've installed Office. You never know when you're going to have to reinstall Office.
Also, if you have files that are locked up in the new Word 2010 file format (.docx), here’s a possibility for salvaging them. Microsoft offers a free Compatibility pack that allows earlier versions of Word (and Microsoft Works) to read and write Word 2010 files. If you have access to an earlier version, this can at least give you back your documents. Some new features of Word 2010 will be lost or converted to straight text in the conversion to the earlier version.
Good luck.