How to access another computer through Internet?

What OS are both of the computers running? What type of connection is currently providing Internet access to the one computer?

Having not mentioned OS, I’m going to assume Windows. Also, by connection via “LAN” I’m assuming you mean via ethernet, and having both of their ethernet ports filled I’m assuming that the Internet connected one is probably using a wifi connection.

If this is all correct, then you should do the following on the computer WITH Internet access:

• Open the Control Panel and go to Network Connections. Depending on your version of Windows, you may need to follow an additional link named “Network Connections” or “Manage Network Connections”.
• You should now see individual icons for each network connection type your computer supports (probably two: “Local Area Connection” and “Wireless Network Connection”)
• You want to right click on the method by which the internet connection is available (wireless) and select “Properties”.
• Within the “Properties” window, go to the “Advanced” tab.
• Here, all you need to do is check the box labeled “Allow other network users to connect through this computer’s Internet connection”.
• If there are more than 2 network connections available, there will be a drop-down list to select on which network connection you want to provide Internet access.