You move your mouth and tongue as if you are gonna make the sounds, just don't exhale the air. They have a demonstration video in the blog post. As somebody else have already pointed out, it's a great tool for interacting with always-on camera devices like smart assistants, makes it a bit less weird.

One cool fact: with silent speech, you can “speak” not only while exhaling, but also while inhaling

Oh I see. So no sound but not with mouth closed