While DynDNS is useful, supporters now have the ability to use a <MyName>.subsonic.org - This coupled with the UPnP functionality added in the last release will eliminate the need to manually forward ports (Providing your router supports UPnP) and to update your dymanic IP.
As agroni1888 pointed out, you will want to make sure it works on your local network prior to diagnosing remote issues. You will first need to know the local IP address of your host PC that runs Subsonic. For the sake of all users who may view this post, I am going to assume you know nothing about basic networking.
Go to START > Run
Type 'CMD' and hit 'Enter'
Type 'IPCONFIG' and hit 'Enter'
The first and third set of numbers are the important ones. The first being the local (private) IP address and the second being the gateway (Router) IP address. Try going to another computer and typing in <IP Address of Host PC>:80 or 192.168.0.x:80 (This assumes two things: 1. You set the port to the default 80 or 8080 and 2. your firewall has been set to allow this connection) - At this point, you should see the Subsonic interface.