Lol, why did you post twice??
With a router, you have a Dynamic IP, which changes everytime the router reconnects. So you need to make a static IP or get a host to redirect your ip.
www.no-ip.com Make a new host there, and dl their client.
As long as it's running, it'll update the ip to the host. So, let's say you made it "admin.servehalflife.com:27015" That would act as the IP. So instead of 1.2.3.4:27015 you would use the admin.servehalflife.com:27015
What's the IP of the computer your running the server off of?
This is for a Dedicated Server. Just load it up, and start the server, be sure to get some decent plugins to make it cool, and enjoyable for players.
If it's a Listen, might wanna do this.
Make a "server" so to speak on your router. Go to your config page for the router, advanced and I think it's Virtual Servers.
Start making a new one, name it like cstrike or whatever, make both port numbers 27015 or whatever you want/need. Do Both, and check Always. And hit Apply, or Ok.
That'll make it so your port doesn't change.
Be sure to type "sv_lan 0" in the console when the Listen Server loads, that way it's not a LAN server, and will be on the public list.