In reply to Duke :
Okay, I think I have the right manual here...
Basically, you have two options. The first is to make your web server available to The Internet as a whole via port-forwarding. The other option would be to require people to connect to your network via a VPN first and then they could access the application. The problem with the second option there is that they'd be able to connect to anything in your home network. If we were talking about a Cisco ASA or something, we could restrict that a little better, but most consumer-grade stuff doesn't support those kinds of ACLs and it doesn't look like this device is an exception to that rule. If it were me, I would set it up with port forwarding.
Question number one is if it is using HTTP or HTTPS. HTTPS could be a problem if you can't generate and install a new certificate for the application web server. If the certificate is for "192.168.1.42" for when you're using it out on site, then when you try to connect to it with a name of "whatever.mydomain.com", it's going to complain about an invalid certificate. I'm pretty sure that most browsers can be told to ignore that and connect anyway, but that can be a little annoying, especially for low-tech users.
Once we know that, we can configure the router. In the setup, it looks like you can go to "Advanced, network, and dynamic DNS". From there you can select a provider, register with them, and then define a dynamic name. That way you'll have a name that you can give people and your router will know when it changes public IPs and will update the DNS servers accordingly.
With that complete, we should configure your application web server such that it gets the same IP address every time. With the system up and running at home, grab the IP address and MAC address from it. In the router, go to advance, network, DHCP server and select "add" in the Address Reservation section. Put in the MAC address and IP address, click the box to enable it, and hit OK. Now, whenever that system connects at home, it gets the same IP address and the router won't give that address to anything else.
Now, you can go to Advanced, NAT Forwarding, Virtual Servers. Here, you'll add an entry for HTTP, HTTPS, or both to forward to the IP address that is now assigned to the web server. Your protocol is TCP, your external and internal ports should match, and if it's HTTP the port is 80, HTTPS is 443.
Once all that's done, anyone should be able to log in to the web server by simply browsing to the name that you created. But be aware that means that anyone would be able to log in to the web server by simply browsing to the name you created! And, of course, if they're able to pwn that box, they're now on your local network and can try to pwn anything in your house. Either keep that thing patched like crazy or (and I am assuming that this is the plan anyway), turn it on when you need to get it prepped and then turn it back off when you're not needing it to limit your exposure.
Hope that helps!