How do I use Photologo Animation on a photo?

Does the animated gif have a transparent background? Or is it a solid rectangle? 

To do what you want is actually very easy.

load the animated gif, and set the workspace to motion

Select frame 1, which should also be layer 1

Increase canvas size to match your proposed background image.

With frame 1 and layer 1 selected either drag or place your background image.  It needs to be right at the bottom of the layer stack, so if comes in above other layers, drag it to the bottom.  This is crucial.

It gets ever so slightly complicated here, so read carefully and follow all steps.  I want to put the NZ flag behind the animated Union Jack and you can see the sizes are not quite right.  You can use Free Transform to change the size, but you need to have all frames selected, or the size change will only show for the selected frame.  That's the tricky bit.

Right so select _all_N frames, and Free Transform the background image. (Ctrl T or Cmd T)

That's pretty much job done, but we might need to do some tidying up.  Your situation will be completely different though.  I can see a bit of background peeking out from behind the animation, but I'll test to see how it works.

First thing is to Crop out the unwanted image area

Now go File > Export > Save for Web (Legacy) which opens this window.

Set format to GIF.  Check the size, and reduce the number of colours if you can get away with it.  The only way to know for sure is to try it, and if it ruins the image, do it again with more colours.  256 is the maximum, so we are not talking about super photo quality.

I can see the background Union Jack peeping out, so I am going to cover that with blue and export again.  Because this is a single layer, we don't need to select all the frames this time.

Now I have a clean animation, although the animated area is showing above the background a touch.

I hope that helps.  You can see it is not a complicated process, but like you said back up the thread, there is very little by way of tutorials for this.