Yeah a capture card like a dazzle or Easycap is one of your options here. As I understand it you need some splitters too so you can share the signal to go from your Wii to your TV and PC at the same time. The reason you have to do this is because there tends to be a bit of lag from whats happening on the Wii, to what you can see on the computer, which is no help when your playing. If you check on youtube their are a ton of videos showing you how to set up.
Another option would be to record your Wii with a DVD recorder.