By doesn't work I mean when I type in the url to access my mac it doesn't do anything, just says the server has stopped responding.
That usually means the port isn't open.
I access the internet using DSL and my router is the new airport extreme.
How would I check what port it is going to ?
You will need to make sure the router is forwarding requests to port 80 to your Mac behind the router. I don't have an AEB but generally, there's a port forwarding option in the router settings. On my Netgear router, I would set it up to forward requests on port 80 to my Mac's local IP address, which is 192.168.0.2 - your's would most likely be different.
You also need to go into Preferences/Sharing and turn on Personal Web Sharing.
Once you have that set up, try going to http://localhost/~<your username> on the mac you're trying to access and see if you get anything. If that works, then you know you have web access locally at least. Then before worrying about dynamic dns, find out your external IP address (google for "what is my IP address") and replace "localhost" with it in the url above.
Did you set up dynamic dns on the router? Again, I don't know how this works on the AEB, but my Netgear has a dyndns section where I specify the dynamic dns server and the host name I'm using. The router keeps the IP address up to date in the dynamic dns server.
This still assumes that your ISP will allow requests to port 80 through. Many ISPs (in the US anyway - I don't know about the UK) don't allow that because they want you to pay for the privilege of hosting your own server.
Also, with web access, your folder needs to be under the Sites folder in your account.
There's an alternative. Since you say you just want to access a folder, did you think about just setting up ssh access? Turn on remote login in Preferences/Sharing and set up port forwarding on port 22 to your Mac. Then you can ssh into your Mac and also use scp to get files from and save files to it. This is more secure, since if you have web access to a folder, everyone else in the world has (unless you set up access control in Apache ...)