If these are PCs (not laptops):
Belkin Router (I recommend Belkin as they are probably the best on the market in terms of value for money)
Cat 5 network cables (1 per computer)
10/100 LAN card (interface card for network in your PC) - this may already be in the PC
What to do ...
Plug filters into BT socket and then from the filter you plug your phone into one side and the router into the other.
Take one of the Cat 5 cables and plug this into one of the ports on the back of the router.
Now at this point you need to know some settings for your broadband - namely your user name and password. Follow the instructions that come with the router for how to set the unit up - it is not that difficult but you do need to be methodical and careful.
Once the router is set up and you can get into the Internet, go to the second PC, take the second cat 5 cable and plug it into the back of your PC and into the second port of the router. YOU DO NOT NEED TO SET UP THE ROUTER FOR THE SECOND PC. It should just work.
I don't understand ...
If there's anything here that you do not feel comfortable doing, then call the services of a professional (not a numpty from PC World or similar) who should be able to get you up and running in a very short space of time provided you have the details of your broadband supplier to hand.
And finally ...
Yes, you can use your 'phone at the same time.
SHARK!