You will need to have your movie on your hard drive in a DivX, Avi, MPG or MOV format. A good way to convert movie files into one of these formats would be to use a program such as Virtual Dub. Virtual Dub is a free program and can be downloaded here.
Once your movie is in one of the formats mentioned you will need to use a program called Wii Video 9.
Wii Video 9 is a free program and can be downloaded here.
Once your movie is in the correct format using the above programs you will need to put the movie on an SD card. The output of the file will not be compressed so you will need to have a rather large SD card. The Wii only supports up to 2GB but I would not use anything lower than a 1GB card. The prices of flash memory have dropped in price so you should have no problem finding a 2GB SD card for around $40.
Now all you need to do is insert the SD card into your Wii and go to the Photo Channel. Select "watch movie" and you are set.