Transform a non transparent GIF to transparent GIF in photoshop

Adding to what you have already been told, it does very much depend on the contents of the GIF, but more importantly, what your desired final result is.  Looking at the circle image in Nancy's post, that's as easy as grouping the layers, and adding a layer mask to the group like this.

With more complex situations, like for instance, where you want a moving character on top of other content, then you might need to make a layer by layer (frame by frame) selection, and delete the background.  That's likely to be quite a job if there are a lot of frames/layers, and if the pixel size is limited, it is is likely to be difficult to get a good result.

Do you have a particular GIF in mind?  Can you come at it from a different direction using something like Fuse?  I occasionally come across animated GIFs where the background layer is separate from the moving content, but that is rare.  What I am saying is that if you can be more specific, we might be able to offer better advice.

When you save a GIF (export for web) you have the option to select a color to make it transparent. note that you only get to pick ONE color, so you will typically end up with halo's around your image where it blends from your image into the original background color.

You're better off getting the original PSD file and then saving it as a transparent PNG.