How do you host a game on halo with a router?

I'm assuming you mean a LAN party. For a LAN party, you have to have multiple Xbox 360s and multiple TVs. Hook each Xbox up to a TV normally, and then connect an ethernet cord from each Xbox to the ports on the back of your router. Once this is complete with however many Xbox 360s you are going to use, start Halo 3 or Halo: Reach on all the systems. Once this is completed, change the network type to LAN for all systems involved (there can be a max of 4 systems with a max of 4 players per system). After this, it should be pretty self-explanatory to get the other systems into the lobby. I think it just automatically finds the lobby, or you have to select the network or something. I've only done this once. I know the first part is correct, but I'm just not exactly sure what it does once you switch all the consoles to LAN.

NOTE: You cannot play via Xbox Live if you are hosting a LAN party. All systems and TVs must be at your house, connected to your router.

Hope this helps!