make sure your router/modem WiFi capable. know if its a unlocked internet(anyone can use it without a passcode) or if you have a password for it. if not make sure that's set up. then through settings on his kindle under wireless/network etc.. you can obtain your internet's IP/bandwidth from there.
In order to connect a modem to your Kindle Fire, you need to have a wireless router, or a device that generates a Wi-Fi hotspot. Therefore, given that you have a router, simply connect it to the Kindle and follow the instructions.