I'll assume there is one computer already working, and you want to add another. So :
1) Does the first computer plug into a router via a LAN cable ?
2) Does the router have more than one LAN port on the back ?
If both are yes, then just plug the second computer into any of the spare LAN ports on the router and it should just work.
If 2 is no, then you'd need a switch to expand the single LAN port to "multiple". Connect the single LAN port on router to the switch, then each of the computers to other ports on the switch - then it should all just work.
If the answer to 1 is no, then more information needed.