Internet on 2 computers

I have one desktop computer with AT&T DSL, which comes in over the phone line. When a guest was here I replaced my modem with a wireless gateway so she could access her laptop in her room at the same time that I used internet on my computer. I'm now wondering, as I search for another housemate, if that person does not have wireless but does have a desktop computer, exactly how can we share internet? Definitely don't want a server as we won't be sharing files, etc., and I don't want to run miles of wires. There is a phone line in that room, which when I used phone lines for telephone service was an "extension", i.e., it rang the same phone number as the one in my room (which now only brings DSL). If a computer in that room has a DSL modem (not wireless) will it work to just connect to that line? We will want to be able to access internet at the same time. I feel so dumb not knowing something as simple as how to plug in! (and the last thing I want to do is call AT&T...that's a nightmare!) Thank you for your help.