Yes, ssh will allow you to login to your system. Kudos to you for going straight to ssh... Most new users try telnet first. Telnet is terrible, and IMO should be removed, becuase it transfers everything, including your passwords, as clear text. ssh uses encryption.
Now, to your problem... It looks like either your firewall is blocking the connection, or you don't have the ssh demon running on the system. You can check the latter with "service sshd status". For the former, ssh needs port 22 open on the firewall. If your computer at home routes through another computer, or an internet router, you'll need to forward port 22 requests to the computer you are trying to connect to.
Read more about ssh at... << www.OpenSSH.org