We have done exactly that in our house. One computer is downstairs, and the other almost directly above it upstairs. The broadband modem is connected to the PC downstairs, and a network card in each computer connected by a network cable which goes throught the floor connects the 2. (If connecting just 2 PCs, a crossover network cable must be used. If connecting 3 or more, a normal network cable and a central hub must be used.) Both computers can access the internet, and both have shared folders that are accessible from either PC. I think we set it up quite easily in one afternoon. We used this site as quite a good source of help:
http://www.homenethelp.com/