You cannot share one phone line between two computers. You need to connect the computers together. If they have RJ45 connectors, then they are ready. An RJ45 connector looks like the connector that goes to the phone line only a little bigger.
It is also possible to connect computers directly to each other with USB or serial cables. Personally, I wouldn't mess with this option. If you do not have RJ45 connectors, you can install a Network Interface Card for peanuts (see sources). With a NIC in each computer, you can connect each to a hub or just connect them directly to each other with a cross-over cable.
Once you have your computers connected to each other, select one to be the "master" and configure it for "Internet Connection Sharing". Use that machine to dial your internet service provider.
With DSL and Cable Internet being available for not much more than dial-up, you might want to consider spending the extra. Two computers sharing a dial-up will be slow. With a cable modem, you may get 100 mbs compared to 56 kbs with your modem. That's a speed difference of 100,000,000 : 56,000.