There are a few things that could be preventing this from working. First, if I recall correctly Wii still requires the special Netflix disk to play any movies, so make sure you have that and it's in the console. If you don't have it, log onto Netflix from your computer and you can easily have it sent to you. It's free, so no worries there.
Now if you have the disk, and you still can't get Netflix to work, make sure that your Wii is registered on Netflix. Again, this can be done from the Netflix website. To check what you have registered to your account just;
Log on to Netflix.
Click "Your account and Help" at the top right of your browser.
Scroll down to "WATCHING INSTANTLY ON YOUR TV OR COMPUTER"
Click on "Manage Netflix ready devices and computer"
Now you'll see a list of devices that are registered to your Netflix account. Make sure your Wii is on there, and if not, then you'll have to re-register your Wii in order for it to work.
If none of this works, then double check your internet connection and be sure your Wii is properly connecting to the internet.
Please leave a comment or rating letting me know if this was helpful or not, feedback is always welcome. Good luck with your Wii, and Netflix.