Playing DVDs on Nintendo Wii: Not Supported, But Alternatives Exist
You cannot play DVDs on a standard Wii. It lacks a DVD drive and the necessary video decoder hardware/software. The Wii was designed solely as a game console.
Workarounds
Standalone DVD player: Connect via HDMI or Composite to your TV. Simplest, best quality.
Wii U: The successor console does play DVDs (and Blu-rays in some regions via update).
Homebrew (Advanced/Risky): Some homebrew apps (like WiiMC) can play DVDs from a USB drive on a modded Wii, but this voids warranty, risks bricking, and is legally gray.
Bottom line: Use a cheap DVD player or a Wii U for disc playback on your TV.