Sure you can.
There are a couple of ways to go to get the 2 PCs to talk (I'm assuming PC's here, if it's MAC stuff,I'm lost)
1) You use a wired connection in each room to connect the laptop to the PC thru a wired router. Hardware costs are cheap and the reliability of the connection excellent. You would need 1 Ethernet connection for each PC (which they might already have) and a router with enough inputs to cable each room into it.
2) You use a wireless laptop solution to connect to the PC. You install a wireless card in the laptop and either a wired or wireless connection in the PC. You then get a wireless router that also supports wired connections. That way you can roam the house while still being able to talk to the 'base' PC. Wireless stuff is a bit more expensive and can be affected by distances and other 'stuff' in the house that you may not be able to control.
Once you make the physical connection, you need to set up the resources on the PC as shared, that allows other computers on the network to use the stuff it owns. This is done thru windows. It's kinda neat to be on the laptop in one room and send a print job to the printer connected to the PC in the other room.
You didn't mention an Internet connection, is that part of the set-up ? I'd recommend a cable modem due to speed and reliability.
You might want to look at places like cnet.com for more info on how to do this. Manufacturers include D-Link, Linksys and Netgear. All have web sites and I'd bet they'd have info on how to set up your network.
I'd say that you should do a bit of reading, then figure out how you want to implement your network. Get the stuff connected and talking to each other first, then set up the shared resources. The key is to not bite off too much at first and be willing to navigate the bumps that always seem to occur. Hope this helps
