If you have ever tried to access a Linux system using VNC, and your host computer wasn’t particularly fast, you may have noticed that things slow down considerably – you definitely know you’re accessing the computer remotely, even if the access is via a local network link. And even if you don’t have that issue, you might want to know about this alternative.
You can install the NX Free Edition server and client from Nomachine and it works great! Note that NX does not work in precisely the same way as VNC – while VNC lets you take control of the current desktop on the target machine, NX lets each login have its own session and desktop. So you could be using your Linux box and let another family member come into it via NX, and each of you would have your own desktop and session.
The best reasonably current instructions I have found are in this article:
Remote Linux Desktops with NoMachine NX
Those instructions are somewhat geared toward users of Debian-based distributions such a Ubuntu, Linux Mint, etc. but there are also packages available for systems that utilize RPM or compressed TAR packages rather than DEB. Most experienced Linux users should have no problem figuring out how to adjust the instructions for their particular distribution.
You may also have a look at remote support tools like logmein, R-HUB remote support servers, teamviewer etc. They work well.