How do the Franks throw the Gestapo off their trail in The Diary of Anne Frank?
The Franks are in an impossible situation...they are forced to live in a very confined area at the mercy of their "protectors" who work in the office down below. The eight of them live a scenario beyond their control, which is awful. Still, they do certain things to "throw the Gestapo off their trail" and minimize the chances that they will be found.
First is the most obvious: they go into hiding. Instead of staying home, Mr. Frank arranges for a place to go. This, by the nature of hiding, throws the Gestapo off their trail.
Second, once they are in hiding, they do not leave the hiding space to go outside (though urge must have been overwhelming!) The best they do is to go downstairs when the office building is empty. Despite the inconvenience (if that is not too weak a word) they choose to avoid the Gestapo by not leaving the building.
Third, and again this is obvious, the people in the "hidden room" do their best not to make any noises that would give their location away.
Fourth, they do clever things like burn their garbage so that they will not have it show up in a can and make people suspicious about how many people are in the building.
These are the main ways that they keep the Gestapo from discovering them. Mostly it amounts to not drawing attention to themselves and suffering silently. They were careful who they trusted and tried not to panic.