Let say computerA is the one with dial up connection, you should only enable Internet connection sharing on the dialup connection on this computer.
After enabling ICS feature, the network card connected to the home network would be assigned a static IP address 192.168.0.1 with netmask 255.255.255.0. This computer will act as a DHCP server assigning other IP addresses in the 192.168.0.x/24 range to other client computers.
So you can simply set computerB to have the IP assigned automatically, then it would get the IP 192.168.0.x and should be able to access Internet.
Good luck..