So If I have a picture and I want to clip the picture like it's a star shape, I put the image on the bottom and the star shape over it, then I go Object>Clip>Set and no problem. But if I do the inverse, with the image on top, both the image and object just disappear.

While I'm at it, this is the effect I am trying to achieve. I have a thought bubble and I want to put an image in it and cut the parts of the image that go outside the bubble. If I try and clip two images, then they both disappear.

Hi.

Make sure you use a path for the clipping object.
A raster image won't work.

As Lazur said, the path (not image) you want to use for clipping has to be on top. If you need to clip more than one image with a single path, you can group the images first and then clip the group. If you want to use multiple paths to clip with (such as a thought bubble and the smaller bubbles leading to it) you can either combine or group the paths first, but they still need to be on top of the image.