Let´s break it down into two steps, an go them one after another...
You should realize, that the IP-address in your LAN is different from the one your router is assigned in the internet (because every "access" to/from the internet ,concerning your computer, is made through the router - in your case).
So if You want someone to connect to You from the internet, you need him to know your routers IP...
As I did mention before, you usually can look up the IP in the router itself (access its menu or via the software provided by the routers manufacturer, or via UPNP -if supported)...
BUT... since your IP address changes dynamically after each reconnect (usually), it will change every day (estimated)... you can "fix" this by going (e.g.) to the link i posted above and create and account, to redirect your IP to some static IP, that You can choose (like google, web.de, msn, etc... )...
After u done this, You and your client are able to use this "name" to connect to each other, because it will be resolved to your IP-address (but u need some kind of software/router setting , which tells the DNS-provider your IP address periodically)...
[It´s not very hard to set things up - don´t be scared of the text amount :D]...
2. Yepp... You need to forward the ports you are using... Either set it in the router interface or use UPNP
http://cplusplus.com/forum/windows/22896/