Quote: "Do i connect to the gateway?"
No, the gateway is transparent, it's just the router or modem's IP so your computer can talk to the router or modem for its own purposes. Ignore the gateway IP.
Quote: "does it automatically find the server?"
If you're using IPX/SPX, sure. But you're using TCP/IP, so you need to make sure the port is open and the client has to know the IP and port.
Quote: "If there is multiple games being hosted how does it know which one is which?"
If a building has multiple apartments, how does the mailman or any visitors know which one? By the apartment number, in this case the port number.
Quote: "How would you join which ip to use."
Could you please rephrase that?
Quote: "Oh yea and when you host which IP should you give everyone?"
Your WAN IP, NOT your LAN IP.
The folloring IP ranges are LAN
Quote: "
10.0.0.0 - 10.255.255.255
169.254.0.0 -169.254.255.255
172.16.0.0 - 172.31.255.255
192.168.0.0 - 192.168.255.255
"
If it's one of those IP ranges, and continuing with the apartment building analogy:
Your computer is an apartment building. Your LAN is the Apartment Complex. The LAN IP is the building number. Your WAN IP is your street address. However, the apartments numbers (ports) are not arranged by building number, they're just randomly jumbled up. Any visitors or mailmen go up to the gates of the apartment complex and say "I want apartment number X" and they get shown the way to that apartment number. The gate is of course the gateway. Remember, apartment numbers are port numbers.
So what you give the people is your WAN IP which is not in the list of IPs you posted.
You can use
http://www.whatismyip.com/ to see your WAN IP. Although that page does not label it as "WAN" but just "IP" because the internet itself is the WAN, so calling it "WAN IP" on the internet becomes redundant.
However, if you have a router at all, you are behind what's called a "NAT"... the NAT is a simple way of saying "a LAN with a gateway to the internet". It's obvious that you are behind a NAT otherwise your LAN IP and WAN IP would be identical.
So what do we do at this point? Grab your router's manual and look up how to set up your port routing. See, every computer can have the same ports open. Lets say, for the sake of explanation, that your game is on port 7000. Every computer connected to the router can have port 7000 open. But only one of them can open 7000 to the internet. This is because the router (the guy at the gate directing people to the right apartment) can direct connections (visitors) to only one port 7000 (apartment number 7000).
Is this making sense?
Remember all that time in school that you complained that math is useless and you'll never need to know trig or calc? Guess what. If you're reading this, you need them.