Internet connections can be shared with software, but they require one of your computers to 'host' the internet sharing software.  The computer that hosts the sharing software can be called a 'connection server' or 'internet PC'.

If you have a cable or DSL modem that uses Ethernet to connect to your computer, the 'Internet PC' will need two network cards in it - one for the modem and one for the local area network (LAN).

As you can see in this diagram, if the 'Internet PC' is not running, the other computers can not reach the internet.  Internet data from the laptop pictured above must travel through the 'internet PC'.

 

Firewall note:  A single firewall prorgam installed on the 'connection server' can protect your entire network.  See the illustration at the top of this page for details.