how does the built-in gallery work?

I must be a bit thick, but I don’t understand how the built-in gallery works?

I’ve got a number of photos that I’ve uploaded and I want to make a gallery page from them. I don’t understand how to do this? There’s nothing in the Gallery tab when I click Add Image. If I add the gallery shortcode to the page, nothing happens. Presumably I have to tell it what photos to use, but I don’t see how?