how do you know if your computer has a network adapter card already?

Most motherboards come with onboard ethernet, so if you're going wired you should be fine, just look at the back of the compuer for a port that looks like this

http://www.mycomputerclub.com/images/ethernet-port...

For wireless you will need a separate adapter, usually that can fit into a free PCI slot like this

http://0.tqn.com/d/compnetworking/1/0/F/3/linksys_...

Or you could always use a usb wireless adapter like this,

http://4.bp.blogspot.com/_FDX1mvf2_7U/TCePJDtGRPI/...

Click on the start button, type in device manager, and hit return.

A window will open showing a list of your computer's hardware devices. If a network card is installed or if the network hardware is built into your motherboard, there will be an item labeled "Network adapters". Click to open that item and see what you've got.