Well, it wouldn't be wise to 'share' a dialup connection as it is too slow when only one person is using it, let alone two. I suggest you get DSL from SBC Yahoo since it is only $15/mo right now and 75times faster then dialup. If you want to make it so you can use the dialup service on both machines, obviously not at the same time of course, you can get a splitter that plugs into your phone wall jack and then you will have 2 phone jacks instead of one and can then run a phone cord to each computer's modem.
As for the home networking part of it, I suggest you get a simple router, only like $30 or so for a decent one. Once you get the router, power down the pc and laptop, turn on the router and then connect the network cables from the router ot the laptop and pc, then turn on the pc and laptop and you're ready to go!
* You also need to make sure that both computers are in the same 'workgroup' or else you wont be able to easily connect to each other through the router. If you don't know what workgroups on computers are, then reply to this message, else good luck and have fun gaming!