I'm not too sure how to do it with a dialup connection... you'd probably have to configure your internet-connected box (the one that does the actual dialing) to be the gateway; set up the gateway for the second box as explained. The big step though is to make your first box do internet sharing. Are both of them Linux boxes? If so, check out this article
and this HOWTO
. Basically what you'll do is set up your connected box to forward stuff to the other box across the network; any incoming transmissions destined for your other box will be forwarded, and its IP address "masqueraded", since that box won't actually be directly part of the internet. Sorta complicated, but it's doable. There might even be a GUI configuration tool with your distribution for setting it up automatically; if there isn't, it should be as simple as installing iptables (which may already be installed) and making a couple edits to one of your configuration files.