Double click on the background layer, but that's not good. Ctrl+J to duplicate the layer. Then create a blank layer above that and use the Clone tool on Current and Below. Always work non-destructively.
The clone stamp can definitely be used on a background layer too, and the same applies to almost any other edit. The only thing you can't do is move a background layer. If you can't edit the background layer, there is something else going on.