What types of technologies are used to link computer networks to create the Internet?

To acutally connect to a network, and be a part of that network get an IP address etc you could use Virtual private network (VPN). To just get access to that network:

Remote desktop connection (RDP)

Remote web workplace (if your on an SBS server)

Sharepoint (though this is just more or less an internal site)

There are a few more ways... but those listed are the only ones I'm familiar with.