I confess to being slightly confused by the original question.
Are both of the computers behind the same router and on the same network (LAN) or are they on two separate networks and you want to connect from one to the other?
ssh is the first step
Regardless of what you are doing next, the first step is to enable ssh (System Preferences » Sharing » Remote Login, which is OFF by default).
If different networks…
Assuming that you want to connect to your personal computer on a different network, the easiest way is to use DynDNS which you can find at http://dyn.com/dns/dyndns-free/. They will give you two hostnames for free, use one for the desktop and one for the laptop.
If same networks…
If you are both on the same network, you should be able to connect to other computer using hostname.local
where 'hostname' is whatever the computer is named in System Preferences » Sharing. I think the default is usually like "John Smith's MacBook.local" or some such. I always change mine right away.
If they are on the same network, you can use File Sharing (although it's still not 100% clear what you are trying to do) or any of the 'remote' options below…
If different networks…
If you are on different networks and want to mount your hard drive, you could use Back To My Mac and file sharing, but I've never found that reliable. You are much better off trying ssh mounted with either ExpanDrive or Transmit.