The PowerPoint Web App is designed for light editing around making quick edits to existing presentations, or creating a presentation from the provided templates and themes.
From what I can tell, insert hyperlink is always disabled in WebKit based browsers (Safari & Chrome), but seems to work fine in Internet Explorer and Firefox. The hyperlink button is only enabled while you are editing text (ie. after clicking on a placeholder that has text). You can also use control+k to bring it up (but you still need to be editing text).
To insert other content, such as pictures, clip art, or smart art, you start by selecting a slide template that has this content. Once you click on insert slide, it will show you what placeholders support content other than text (by showing the "content insertion" icons). If there is a content placeholder on the slide, insert picture, clipart, and smartart will be enabled even if it's not selected.