This posting is older than 6 months and can contain outdated information.
Thanks for asking.
Here's the steps to success:
1) Set up an account at DynDNS and install their software so that your 
computer's IP is now reachable via the domain name
whateveryousetup.dyndns.org
2) Make sure, port 8888 is reachable from outside. That may include 
adding  a special rule to the OS X Firewall (see the FAQ for a guide) 
and - if you to connect to the internet through a router - adding a 
port forwarding rule to your router's configuration (should be 
detailed in your router's manual).
3) Make sure that Remote Buddy and your computer are running and that 
the internet connection is active.
4) You should now be able to reach the AJAX Remote through the 
Internet via
http://whateveryousetup.dyndns.org:8888/
I'll not be able to provide support beyond this, though, as support 
for building and administering networks is beyond the scope of this 
product.
Here's a tutorial on setting up DynDNS:
http://www.nonstopmac.com/2005/12/give_your_mac_os_x_computer_a.htm
If you use a router, this may be of use:
http://www.portforward.com/
And for typical DynDNS problems articles by DynDNS are available right 
on their website:
http://www.dyndns.com/support/kb/why_cant_i_connect_to_my_server.html
Hope that helps.
Best regards, 
Felix