wired router can i unplug cable

I am new to broadband.
I want to connect 2 computers and am exploring wired/wireless routers.
If I have a wired router, do both computers need to be connected to the router at all times?
Or can I unplug one when I don't need it and just plug back in when I want to go online? The second computer will prob only go online maybe once a week, so I don't need it connected at all times (and it is in a different part of the house so I don't want to ave wires trailing all the time)
I know I could go wireless, but I want to explore the wired options first.
Thanks
T

Yep, with Ethernet CAT5 cabling, you build a network in a "star" configuration and each computer has its own connection to the network, which can be connected and disconnected without disturbing other machines.

You might want to consider Devolo, which uses your mains wiring to join up a network.

thanks Xris, that's what I wanted to know