.Wireless modem|-------------- DS
Whether you're using cables to connect to the internet or using a magic modem which sends internet signals through the air, your wii will be constantly conected. Obviously it helps alot more if the you have one of those "magic wireless modems" because then no matter where your wii is in your house it can be online and you don't have to worry about those silly cables.
P.S. It's quite easy to get a free wireless modem if you call up your internet service provider (ISP, the company that supplies you with the internet thingy), and just bargain with them. Say you'll switch to another company if they don't give you one. That's what I did.