Installing 2 NIC Cards on 1 Computer

Currently there are 4 computers on a network. These cards and network are part of a private network for a car manufacturer, amd we are not allowed to change any settings. internet explorer is used to browse this private network. I want to add another NIC card and connect thses computers to the internet through a high speed cable modem and the linksys cable/dsl router. Can a computer have 2 network cards installed and will these computers have internet access capabilities. What is needed tobe done? Thanks.