By default, most routers will block traffic from outside the local network. If you want to have access to something on the LAN side of the router, you have to configure the router to allow that traffic to pass through.
One way is to open up specific ports (like, say, 80, if you are hosting a website). Traffic hitting the router on port 80 would then be allowed into the LAN. The second part of the port-forwarding configuration is to tell it which computer that port 80 traffic should go to. If you were hosting a website on 192.168.0.100, you'd forward 80 to that address.
Another way is to use a DMZ. This is functionally equivalent to opening up ALL the ports on the router, and sending all that traffic out a LAN port. It has its uses, but this is probably not ideal for you.
DynDNS, as Alen mentioned, is an online service that will pay attention to what your public facing IP address is, even as it changes. Instead of needing to know that IP, and entering that into a browser or terminal, or whatever, you enter a domain name (like myhouse.dyndns.com, or something like that) that is always pointing at your public IP.
In your case, I would set up a free DynDNS account, and configure port-forwarding on your router.