You can set up a network. The most simple network consists of only two computers. You can use this network to share files, a printer, or another peripheral device, and an internet connection.
Two computers
a cord
You can buy a firewire cord. That is the fastest and easiest way to connect two computers.
wireless
An HDMI cable is not designed to connect two computers together.
yes
linksys
Cross cable.
You can connect them with an ethernet cable, or by WiFi if they have wireless cards.
Buy a lan router, they can be used with lan cable or wireless to connect all your computers through a network. If there are only two computers that you wish to connect then you only need on lan cable which you connect in the back of each of those two computers to create a network.
I believe that it is possible to connect to computers to one monitor. I have worked with brand new LCD monitors with two inputs - one DVI and one VGA. The monitor auto-senses which port is being used. So in theory, use the auto detect button on the front of the LCD panel to switch between computers.
The safest and easiest way to connect computers across time is with a VPN. A VPN is a virtual private network that makes a tunnel between two or more computers.