Hamachi is a Zero-Configuration VPN (Virtual Private Network) service. Unfortunately getting the Hamachi service to work well in Linux requires a few steps, and until recently it was more difficult. Here is my guide for how I get it working with as few hurdles and hassles as possible:
There is a progam called 'Haguichi', which supports the Hamachi protocol and is an up to date program. It has a PPA available for Ubuntu. Go and add the PPA to your system, and then update and then install Haguichi.
Hamachi backend itself must be installed, which must be downloaded, compiled and installed. You can grab the official legacy client from here: http://files.hamachi.cc/linux/. To compile it, extract and run 'sudo make' which will auto-install.
After that, the program 'tuncfg' must be started. Running 'sudo tuncfg' on command will do this. (NOTE: That is 'tuncfg' NOT 'tunecfg'.)
If you have connection problems, try disabling your computer's firewall. This is probably blocking the Hamachi port. (I have no idea which port it uses.)