How do you deal with NAT when creating network applications?

I can create programs that talk to each other as long as they are running on computers in the same subnetwork. But I can't get them to work on the internet, of course, using private IP addresses. So I have done a few hours of googling and I understand this whole problem a little bit better but I still need some help. Let me explain the problem as best I can. I am on a private network with a private IP address. When I send and receive info across the internet my computers private IP addresses is translated (NAT) by my router to a public IP address. This is done because of the limited number of IP addresses in the world, because it makes configuring networks easier, and I think it has something to do with UPNP (I'm not sure). I found the following code on codeproject.com: string myIP = "an ap address"; IPEndPoint ipep = new IPEndPoint(IPAddress.Parse(myIP), 8000); Socket server = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp); server.Connect(ipep); if I use 127.0.0.1 or if I get the private IP address of the computer running the server application and use that as the IP address for the client application to connect to (client running on different computer which uses same wireless router as the server application's computer) then it will work. But let's say that I wanted you to be able to run my program on your computer. If I look up my public IP address and set myIP = "my public ip" will that work? I can tell you that it does not work if I do that on another computer connected to the internet by this router. It's pretty obvious that I am confused. I thought this would be a pretty common thing but I'm having a lot of trouble finding good information about it.