After having transformed the modem into a router, how do I share the Internet with the other computers in my home or office?

You will need to buy a hub or a switch and connect the modem/router to one of its ports and each one of the computers to an available port in this equipment, using a twisted pair cable in a pin-to-pin configuration (the renown network blue cable). After being transformed into a router the modem starts working as a DHCP server, so you just have to configure the network in each machine to the automatic mode and the modem/router will configure the network for you.

What will be the IP of the machines?

As we said, the router will work as a DHCP server, thus it will automatically supply the addresses of the machines (something like 192.168.x.x), so configuring the machines to the automatic mode will allow the router to configure them automatically. The machines will access the Internet using a single public IP, which is the IP address supplied by the telephone services provider. Since each machine will use a magic IP (addresses like 192.168.x.x and 10.x.x.x are called "magic" because they do not permit the direct connection to the Internet without using a router), the modem/router will also become a firewall, preventing hackers to access the machines in your network. In other words, besides the comfort the modem now offers working as a router, you also have more safety.