Is there a simple way to connect my computer
 

in the living room, with my daughters computer in her bedroom (both redhat 8.0) and connect to the internet simultaneously?

I would suggest getting a router. Nothing fancy like a cisco or anything like that. There are some really cheap routers out there and they do the job of home networking very well. Its also nice to have that extra level of security that a router offers. You could also buy another nic card and do it that way but by the time you set all that up you'd realize it was easier to buy a cheap router.

If I buy a router, would I need a seperate phone line to connect to the internet, or could I share (piggyback) on the main internet connection for computer 1? Is it possible for two machines to surf the internet (56k) simultaneously or is this only possible with High speed access.

Will this switch (router?) do the trick?

http://dlink.routerreviews.net/LG/el...B000023VUE.asp