VPN is certainly possible. Try a google for 'remote access'. Dont know of any free services though.
A solution I use at work requires a PC 'in house' running a remote access program - the one we use I cannot remember, but there are several available. If you want to know, post here and I will reply when at work !
You run the same software on your remote PC and you see the desktop of the local (networked) PC and control it with your mouse and keyboard, so it is exactly as if you were sitting in front of the networked PC and can operate at full LAN network speed - say fast ethernet or Gigabit. Since only the keyboard and mouse movements go one way and the screen refreshes go the other way, you do not suffer at all from the limited IP speed between the remote PC and the local PC (follow that?).
Other approaches (VPN for instance) suffer the problem that ALL network traffic into your LAN can only be as fast as the remote connection, which varies from dial-in to broadband. So successful use of VPN requires one of two things - either a very fast (e.g. fibre optic) connection, or you attach to a server software solution running on your server, and the remote PC is only a client, so ends up again only passing keyboard, mouse and screen refreshes.
It all depends on what software you need to run on your local LAN, see?