Clicking on the "Add a Photo" button should pop up a file browser that lets you select a photo from your computer. Clicking "Attach an Existing Photo" should pop up a small window that lets you select a photo from your user account. I just tried it and it's all working as far as I can tell. If one of those isn't happening for you, do me a favor and let me know what operating system and browser you're using, and I'll check to make sure there aren't any bugs specific to that setup.

Also, sometimes 3rd party software can prevent pop-up windows from appearing, especially ad blocking software. If you have something like that, try temporarily disabling it.