How to have a internet connection between two computers

I have a computer in my living room that gets internet from a grey modem. I have a computer in my room that isn't connected to the internet at all. Now, I do have a wireless router in my living room also. Could I somehow give off internet to the computer in my room and create a certain kind of home network? Please tell me what you can, it would be helpfull.

To get internet from your wireless router you will need a wireless adapter for your computer in your room, or you could run an ethernet cable from your living room to your bedroom. Running a ethernet cable would be the cheapest and probably easiest depending on the distance.

Connect modem to router, connect with computers to the router. Can't tell you more without details (how you get your net, - ADSL, cable - what model your router is, etc).

So what you want is to get wireless access to your internet? If you have a wireless router already you can simply hook it up to your dsl modem via ethernet and have your systems connect to the router via wifi. This guide here can get you set up.