How to make a computer invisible in network?

Without credentials on your computer, the only thing that a spectator can do to your computer is read its name in the Sidebar. They cannot open, read, or edit any files on the computer. If you share your drive, then they have essentially drop-box privileges. It is a non-trivial matter to allow a remote user to gain access to your Mac.

 

sys prefs - sharing - OFF
firewall - advanced - stealth mode

 

in the sharing prefs disable everything

The main ones someone could use to access your computer is file sharing, windows sharing, screen sharing, remote login (ssh) and remote desktop.

To do any of this they would need to have a user account setup on your mac, the only real way of doing anything malicious i can think of is remote login with ssh, but if remotre login is off i think that turns ssh of.

As said by modernape if you enable stealth mode under security>firewall>advanced, that will stop your computer responding to pings and portscans etc.