You need a SD card and something that can connect the SD card to your computer(unless your computer already has that built-in-thingie).
Open up your town map and press the 1 button on the Wii Remote.
Save the picture to the SD card.
Connect the SD card to your computer.
Open up the file in your card called "DCIM". In there you'll find every snapshot you've taken in City Folk.
Go to imageshack.com or any other picture uploader site.
Click on the Image button while in posting mode and paste in the link to your uploaded image.