Screen Share over the Internet

The easiest way I know to do this is to have a MobileMe account. It has a feature called 'Back to my Mac' that is made to make this work easily.

It may be possbile without a MM account, but I'm not a network engineer so I'd have no idea on where to begin on that quest. All I know is that I have MobileMe and it works. (Your home router plays a part in this as well, some work with it and others don't. I own an Apple router so it's not a problem for me, but I know it won't work at my parent's house with their Verizon-loaned router. So google up 'Back to my Mac' troubleshooting tips and see if you can learn anything there before you pay for anything.)

MobileMe does cost money, but be sure to get it from Amazon.com. There are people selling it there for less than the $99 list price. Usually because it's last year's box, but the code is still just as good as any new box. You can usually save a few bucks that way.

what kind of error message are you getting?

make sure you follow the guidelines here:
http://support.apple.com/kb/HT2084?viewlocale=en_US

note: your router either has to support NAT-PMP or UPnP

following ports have to be enabled:
TCP 443 (signing into MobileMe and enabling Back to My Mac)
UDP 4500 (for connections between machines)

Back To My Mac has been hit or miss for me... just been easier for me use VNC/ScreenShare (with a SSH tunnel).

cheers...