A LAN party means that all the PCs are in your house, connect to your router. That's what LAN stands for: local area network. So I assume you are not referring to playing with others outside of your building, from the Internet. Let me know if that assumption is true.
Since I don't know anything about your router, this will be a very general answer. All you should need to do is to connect both of your PCs to the back of your router, assuming your router has four or so Ethernet ports in the back of it. Or if it's wireless and your PCs are connecting to the router wirelessly, then you're already connected and should be able to play with each other without a problem.