I ordered a new desktop computer, but my mom wants to use the old one for herself. I wanna be able to connect both computers to the DSL internet. I hear you can do it with an ethernet network, but I'm not sure how to use it or with what hardware. Help me out here.

Use a router. They are really simple to set up.

Yes; thats true, U can use a router to set up a multiple internet connection, thats what I have at home; and, if U are going to use a laptop or do not want to have wires over the house, it is better to use a wireless router.

ok. use a router. do not use a hub. they may tell you to get a hub. but it wont work. router is simple tho.

you plug the Ethernet from the dsl modem (the little box that the phone line goes into) then plug it into the port on the router that says internet. (this little Ethernet port should be on its own. its not generally next to all of the other ones.) then plug your computer into the other ports. they will generally have numbers above them.

yeah, routers are easy. I've got like 10 computers on my LAN works fine.