The easiest method is to make sure your computer is not broadcasting any Bonjour messages about what services are available on your computer by turning off the services.
In terms of the Finder, make sure File Sharing, Remote Management and Screen Sharing are all unchecked and your computer won’t appear in another user’s sidebar. If it has already shown up on the other user’s sidebar it may not disappear right away but nothing will be accessible. This won’t prevent it from appearing elsewhere (eg. if you’re sharing printers then it will show up in Print dialog boxes).
The other alternative is to turn off Bonjour all together which requires a restart. Apple has postedinstructions on how to do this. Coles notes/faster version:
sudo /usr/libexec/PlistBuddy -c "Add :ProgramArguments: string '-NoMulticastAdvertisements'" /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist
To turn back on:
sudo /usr/libexec/PlistBuddy -c "Delete :ProgramArguments:2" /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist
After completing that run the following command as well to make it take effect:
sudo launchctl unload /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist
sudo launchctl load /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist