Instructions
Disconnect the microphone and then re-connect it to the USB ports in the back of your Wii. Sometimes the microphone doesn't connect due to a power irregularity or other issue. Simply unplug it (while the Wii is on) and then re-plug it in and try again.
Check the USB plug for dirt or other material. If your USB plug is dirty, it could hamper the connection or create "static" sounds when connected. Use a lint-free cloth to wipe down the USB connector and then try using the microphone again.
Look for problems with the cable. If the microphone's cable has been damaged, the microphone may not work correctly. If you notice a small break in the cable housing, repair it with electrical tape and try again. If the cable is severely damaged or severed, you will need to replace it.
Try connecting the microphone to a PC. The Wii microphone is also compatible with PCs, so if you can successfully connect the microphone to a computer, but not to your Wii, the problem lies with your console. In this case, contact Nintendo Support for more help. See the "Resource" section for a link to Nintendo support.