I have done this on the server by installing a special server-side version of Adobe PDFCreator which allows you to drop a file into a folder and pick up the PDF from a different folder. The client uploaded a Word file in the usual manner and the server-side script dropped it in the folder. The client was then shown a link to grab the PDF.
If you want to transform on the client you'll need each client to install a Word to PDF add-in. These usually involve printing to a special print driver that actually transforms the printing instructions to a PDF. For this you'll need to automate Word using client-side script and have low security settings in the browser to allow opening and saving files from the client's hard drive.
Joe (Microsoft MVP - XML