Hopefully, I'll be able to fill a very frustrating void that I've encountered. Many sites claim that streaming video to your Wii over a local area network is easy as pie, but I have yet to see detailed instructions. So, here you go!
Step 1: What you'll need:
The Homebrew Channel.
MPlayerWii, loaded properly onto your SD card.
On your computer, you'll need to install VLC, a small but full-featured media player.
You'll also need to find the local IP address of the computer(s) you want to stream from.
To do this, open a command prompt and type "ipconfig." This gives you your IP address. Write it down!
Now, open the "mplayerwii.conf" file on the SD drive, and add a line that looks like this:
"stream = http://[your ip address]:8080/"
So, my line would look like this:
"stream = http://192.168.2.2:8080/"
Save that file, put the SD card into your Wii, and load MPlayer from the Homebrew Channel.
Step 2: Prepare VLC for streaming
Select the Media menu, and click on "Streaming..."
In the open dialog, select the file you want, and click "Stream". The Stream Output dialog will open automatically.
Check the "play locally" box if you want the file to play on your computer simultaneously. It's good to do this the first time, to make sure everything is functioning properly.
Also check the "HTTP" box. Leave the port set to 8080, and keep the "Address" box blank.
Next select "XBox" from the profile menu, click "Stream," and you're ready to go!
Step 3: Connect the Wii!
If the stream doesn't load, you'll need to add a web interface to the player. To do this, go to the Tools menu, and select Add Interface -> Web Interface. Select the IP entry again, and it should work like a charm.