It's simple. Really:
Set up a free account and you can create your own hostnames with your router's current ip address. The even provide software to update the address when it changes.

With that done, all that your client needs to know is the hostname to connect to your router. If you've set up port forwarding correctly, they'll connect to your Mac. Then if they have the correct username & password...

I'm sure you're right but there is a small avalanche of material to read with this and it's yet another day frizziled away creating nothing . Need a big glass or two of the Vin Rouge.
Thanks again
Peter

Read a little, then try it. If it doesn't work, read some more and try again. Either you can connect or you can't, but you're not going to break anything. ;)

Hopefully helpful information
 

I am about to set this up for my brother in law. My network is:

Internet-----Router-----Mac

OK, that's a bit simplified, but the key part is the router. I'm at home, and I have a dynamically assigned address (meaning, it changes). So as was said earlier, I have a service (EasyDNS in my case) that my router speaks to, so that anyone looking for my domain will end up at the correct IP address for my router (my router says to EasyDNS's servers "Hey, my IP changed, here it is" and EasyDNS's servers say to the Internet "Hey, if you want his domain, go to this IP address". Because computers use the IP address, not the name.)

So that takes care of the ever changing IP address on the outside. On the inside I have each computer set up with a "Static DHCP" address, which means the router looks at the MAC (or hardware) address that it sees at a low level, and says "OK, that one gets this IP address", say, 192.168.1.42. That takes care of the ever changing IP address on the inside.

Next, my router is set up that afp connections aren't blocked, but instead are forwarded ("Port forwarding") to my Macintosh. I have many machines inside, but the router sends them all to my Mac. I could allow anyone to come in on the ports, but I don't need the hassle (who knows, maybe malcontents would check, find that guest login was on, and fill up my hard drive with uggy stuff via the drop folder). Instead, I turn it on to a single computer only when I need it, then I block it again at the router.

Hopefully you are with me so far. And a bit of terminology: My router is more than a router, it is a firewall, and a switch, and a DHCP server, and a wireless access point. I think it makes a good single malt, too. I'm running "Tomato", an open source, highly recommended replacement for Buffalo's original firmware.
http://www.polarcloud.com/tomato/

Assuming you pretty much followed me, the only thing left is how to open up the firewall. The idea if you want to connect to an IP address for a certain service you have to contact that IP and say "I want web service" or "I want AFP". "Ports" are what does this. Ports 548 and 427 are what AFP uses (web service (http) uses port 80). So I set up the router such that anyone connecting to it on those ports gets to my (certain) Mac which then happily serves it up.

OK, I glossed over something that may be important to you. You want any Mac to be seen. What you need, then, is for every machine to be reachable from over the Internet, which means it has to have DNS.

Thanks, I've actually got the whole thing and I was getting it earlier but kept getting refused connection because I had a dynamic address and that confused me and I was convinced that i wasn't 'getting it '. My isp won't give me a static address.
Each mac has a manually assigned local ip address and I have been able to see my macs from outside my local network with Remote access but couldn't connect. The DNS service, suggested earlier looks like it would do the trick but I need to study it instead of poking around.
Peter