Download the movie to your PC. It should be noted that downloading movies, or "ripping" content from studios without paying for them through a legitimate site (like itunes.com) is a crime. You can be prosecuted and face a stiff fine and jail time. However, assuming you rightfully paying for the files, download them.
Convert into the correct format. In order for you to play movies on your Nintendo Wii, they must be in one of the following formats: DivX, Avi, MPG or MOV. (Some files may already be in these formats.) If not, download "Virtual Dub" (by searching in your favorite search engine). It's free and it will make sure your files are in the correct format.
Download Wii Video 9. This is the integral program which will serve as the program which actually plays the file on the Wii. It is free to download, and literally only takes minutes to open.
Purchase an SD Card. The bigger the card the better. But make sure it's at least 2GB. These can be found on ebay, or at Circuit City or Best Buy.
Insert SD Card. Place the SD card into your computer and save the video file (which should now be in the correct format) on the SD card.
Place SD card in your Nintendo Wii. Place the SD card in the wii. Then turn the setting to the "photo channel," use your controller to press play and sit back and enjoy your movie! Congratulations, you have just learned how to watch movies on your Nintendo Wii.