router and switches

I AM ONLY A NOVICE,BU T ICAN TELL YOU THAT A ROUTER WILL,BECAUSE I JUST SET ONE UP.HAVE THREE COMPUTERS ON IT.LINKSY IS THE NAME OF IT

A router is a box that determines the path taken by a TCP/IP packet to get to a another network with another IP address range.
A switch directs ethernet packets to the correct interface using MAC addresses it has learned by "listening" to its own ports.
A gateway is an interface on a router that you direct computers to in order to send data to another ip address range.

This is a very brief and technically incomplete description as many other replies will inform you.

As for sharing an IPaddress, every ip address on the entire internet MUST be unique. (with the exception of private addresses).

To share a number of ip addresses from the same ip address range connect the computers together with a switch.

This is also a very brief and technically incomplete description, I could go on about private address ranges but I think that would be beyond the scope of your question.

A router is a device that transports routable protocols from one network to antother.
A switch is like a hub, except it provides a constaint speed to each port on the switch, plus there are other differences, such as being programable etc.
And finally a gateway is just an interface to connect two networks together.
If you talking about sharing an IP for a home network able to access the internet, linksys makes a great devices just for that purpose.

The definitiions of these devices (and a lot of other technical terms) can be found here:

www.whatis.com

The sharing of Internet ip addresses can be accomplished either with hardware (a router or switch or hub) or software designed (programmed) to route/translate (also known as Internet Connection Sharing (ICS) software or proxy software).

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