Here are some basic instructions for streaming media from TwonkyServer to a Nintendo Wii:
1. Make sure your Wii is connected to your home network.
2. Open the Opera browser on the Wii. Itâ€™s available as one of the channels from the main menu.Note: If the Opera browser is not loaded onto your Wii, you can purchase it from the Wii directly and download it from the Wii application site.
3. Once the Opera browser is open, enter the following URL: http://ip-address-of-Twonky-Server:9000
This will provide a Flash interface, which can be used to navigate your media server and select various types of content which can be streamed to your Nintendo Wii.
Keep in mind that the Wii has a relatively low-powered processor. For that reason, it may not be possible to stream every type of video to it.
P.S. Thanks to Jim Pfeifer for providng this answer.