Whenever I want to add an image to my answer, I go to Google Images and save it, but when I post it, it says "Sorry, we do not support that image type." How can I get around this problem?

You can go into the Windows Paint program (if you use Windows, that is), and click File, click Save As..., and then save it as a JPEG.

Maybe try making sure it's saved as jpg or one of the ones it says it has to be?

Sometimes, when saving an image from google, if you don't specify the extension it can save it as an HTML file.

You need to make sure that the file is either a .jpg, .gif, .png, or .bmp.

I'm FAIRLY sure it supports .bmp files. I could be wrong, though. If I were you, I'd stick with .jpg, it's the most reliable.

You should save it in a different image format. Sometimes, saving an image from the internet might be a HTML file. When you save the image, it might be best to check what format its on and change it to something desirable. If you're using GIMP or Photoshop or anything else, it would likely save as a GIMP file or a Photoshop file. Just change the format on some sort of photo manipulation program (like the ones stated above) and go to [File->Save As].
Its best to save it as a .jpeg file or .png file.
(The .jpeg file compresses it and makes it blurry but the .png file keeps the look including transparency, however, is a bigger file than .jpeg format.) A .gif format should work too.

I'm not sure what sort of image format Fanpop supports. Though, maybe its best to find an article about it.

Well, When your picking the images,
You have to change the type mode set to "All Types [*.*]", Then go to the Image directory, Double click it or single click it then click "Open", Then just wait till it get's uploaded :)