One way to do it is to run sshd (the secure shell daemon) on your home computer. Assuming you have cable or DSL internet access at home, you will be able to ssh into your home computer from anywhere (provided your firewall, which you should definitely be running if you have cable or DSL, has port 22 for sshd open).
If you want it to look just like you're using it at home, with GUI and everything, you will probably need to run some kind of XFree86 server on the machine you are using to connect. Easy if that machine is already a Linux box - if not, you can get commercial or free alternatives (Cygwin being a free one for Windows). If you have an X server going, and use ssh, everything will probably work automatically (though it's a little trickier with Windows).