Linux (unlike Windows) has all of it's hardware adapters on the Kernel. When new hardware is installed it should show up in the lshw command. In this case if this is a new network card connected to PCI-E slot, it should show up under PCI-E.
Look for Logical Name of the New Network adapters. If you desire to change it you can do that at: /etc/udev/rules.d/70-persistent-net.rules
Update /etc/network/interfaces file for the new network adapter. If you already had eth0 and now want to include eth1, then add that to the file.
Make sure you connect a LAN cable to the new network card and either reboot the system of do an ifup eth1 as root.
Do an ifconfig to see the new network adapter show up with it's DHCP or designated Static IP address.