I don't think QuickOffice is something you can start on its own.
Downloaded files are typically stored in the /download folder on the memory card. To view this folder with stock Android you can open the browser, then goto Menu -> More -> Downloads. Tapping on a file there should open it in the appropriate application.
To explore the rest of the memory card you'll need a file manager type application. There are too many of these in the Market to list them all, but a few are Astro File Manager, Linda File Manager, and File Magic. Even though they recently started including ads in the free version of Astro, it's still my favorite, though I'm now looking at File Magic.