You need to make the background transparent.
The easiest way to do that is to make the background a solid colour that doesn't appear in the picture. (In the case of the picture of the dog, I would probably go for blue).
I'll demonstrate with this pic

Then you need to select the transparent colour tool:

A pop-up window will probably appear that looks like this:

Select yes.
Then this window will appear:

The solid background colour is generally the only option you get to make transparent. The tolerance level will adjust how much of the colour blue is made transparent - a low tolerance setting and there may be faint lines around the picture, a high tolerance will sometimes remove colours in the picture, or make outlines less defined - you can preview what it looks like, and if the tolerance needs further adjusting, you can just keep going until the preview looks good.
This is what it will look like in Photo Filtre

After that, the picture needs to be saved in GIF format, or you will lose the transparency.
This is what it will look like when posted

I reject your reality and substitute my own. ~Adam Savage