So, you've got subsonic set up so you can access it from any computer in your home by just typing in 192.x.x.x:8080 or 10.x.x.x. However, these are merely internal IP addresses.
In order to access your computer remotely, you'll have to do two things: open up your port to the outside world and find out an internet address for your computer. In the new version of subsonic, you'll be able to forward your port automatically (using UPnP) and access your subsonic server through a gosubsonic.com address. However, until that time you can use these instructions below. Also, they provide an alternative in case you don't have a router that supports UPnP port forwarding or if say you don't want a gosubsonic.com address.
Forwarding your port
So first thing you'll have to do is to open your port to the outside world. This depends greatly on what type of router you're using. First you'll have to find out your internal IP address. If you're on windows, run "ipconfig" on the command prompt. For linux or OS X, run "ifconfig" look for a string that contains four numbers and three periods. For an internal IP address, the first number should probably start with a 192, 10, or 172.
Now go to your router's configuration page and forward port 8080 (or whatever port subsonic is on) to your computer's internal IP address. If you have to forward a range of ports, you can just do 8080 to 8080 usually. If you have to choose an outside port to forward to an internal port, use 8080 for both.
Addressing your computer from the outside world
To access your computer from the outside world, you'll have to find your internet IP address. This is a number that is unique to your computer's connection to the internet. An easy way to do this would be to go to ipchicken.com where it'll have your IP address in blue.
Now if your port forwarding is set up correctly, you should be able to access your computer using that ip address. Let's say your ip address is 97.74.125.134, your port is 8080, and the path to your subsonic server is /subsonic, you'd type http://97.74.125.134:8080/subsonic to go to your server. If you have the SUBSONIC_CONTEXT_PATH variable set to /, then it would be just http://97.74.125.134:8080 and if you have your port set to 80 (the default http port), it would just be http://97.74.125.134
What if my address is dynamic?
Ok, so most of you either 1) don't want to memorize a string of digits or 2) have a dynamic IP address. A dynamic IP address means that every time you disconnect and then connect again to the internet, you're given a new IP address. If you're not paying extra to have a static IP address, then you probably have a dynamic IP address.
The easiest, best way to deal with these problems is to donate to subsonic and get a gosubsonic.com address when the new release comes out. It's under the network panel under settings (versions 3.9+).
However, you can use another service like dyndns.com if for whatever reason you don't want to do this. Go to dyndns.com and sign up for a FREE account. After you've set that up and signed in, go to the Services page and under Host Services click Add Hostname. Here you can pick a subdomain, and a domain from the drop down that you can have resolve to your computer. You'll see an input asking for an IP Address and a link letting you automatically fill in your current IP address. Use the link and click save.
Now, you'll probably have to wait a bit but eventually you'll be able to go to tacgnol.dyndns.com:8080/subsonic (or whatever your new address is) and access your subsonic server. In order to keep this address automatically up to date (remember that your ip address changes whenever your cable/dsl modem loses its connection) you can use one of the clients on dyndns.com's update clients page:
https://www.dyndns.com/support/clients/