So I am guessing you have an ADSL modem that you are planning to plug into your Wii? Are you planning to go wireless or wired? Also, are you planning to have a computer connected to this as well, or just your Wii?
If you are just connecting your Wii to the ADSL modem wired, you will need the Nintendo USB to ethernet converter and an ethernet cable, just plug the ethernet cable to the adapter and the modem and plug in the USB part to the back of the console and do the interent setup on the Wii, if you are planning to have your computer connected to the connection too, you would either need to get a wired router or you will need 2 ethernet cards, one to plug your computer into the ADSL modem and another to plug your Wii into your computer, also you will need a crossover cable to plug your Wii into your computer
If you plan to use a wireless connection, either you will need a wireless router or a Nintendo Wi-Fi Connection dongle, if you use a wireless router, just plug your ADSL modem into the router and connect everything to the wireless router, if you use the Wi-Fi dongle, plug youe ADSL modem into your computer and install the dongle on your computer and setup the connection on the Wii