First I check to see if it is integrated into the motherboard or a pci card. You can usually tell by the location on the back of the case. If it's in one of the lower pci slots by itself, you know that its not integrated or (on board).
If thats the case, I open the box and remove the card to have a closer look at the numbers on the chipset.
Write those down. Example: RLT8131A is a Realtek card.
Once the have the chipset model #, do a Goodgle search for the drivers, (usually at their website).

Another method, is to download and install the Belarc Advisor software (freeware). This will tell you what is inside the box. You can get it here.
http://www.belarc.com/free_download.html

Best of Luck