well yes and yes
what you want is a lot more work than the sharign the interet connection with a router - here's my take on it:
point1 ) but the best way to get 2 computers on the internet is to use an ethernet router - most UK ISPs now provide routers to connect to the internet. (BT home hub for example has 2 ethernet conections) or if it only has one ethernet connection (i.e. virgin meida cable modem) you need an ethernet swtch (bit like a junction box/extension lead for ethernet connections) where you connect the PCs to the ethernet modem to access the internet.
then all you need to do is connect both computers to the router with ethernet cables. and setup the ethernet connections using the 'home network wizard' in the control panel
point 2) If you want to get one computer to 'go through' another computer then you still need to connect the 2 PCs together, if the 'internet connected' PC is usiing the ethernet to talk to the internet then you will still need a ethernet switch to connect all the PCs together and then you might as well do point 1. but if you are using the old USB modem - then you can connect the 2 PCs together with a 'cross over' ethernet cable ( a specail type of ethernet cable) then you have to setup the internet PC to allocate IP addresses and also 'share' its internet connection.-
to share the internet connection go to the conotrol panel of the PC with the internet and click on "home network wizard" and follow the instructions - there will be a step that asks if you want to share the internet connection. then do the same on the other PC but tell it to use the shared copnnection.
performance wise - the PC that is 'sharing' its internet connection in point 2 will be doing more work handling 2 lots of internet traffic.