A handy trick is to right-click the unknown device in Device Manager, then go to Properties. Click on the Details tab and make that Hardware IDs is selected. You should see something like:
The red text is the Vendor ID (preceded by VEN_) and the orange text is the Device ID (preceded by DEV_).
Armed with this info you can visit http://www.pcidatabase.com and do a little searching. I have found a few newer devices that don’t exist there, in which case you can plug both IDs into Google and let the magic begin!