The incognito mode, which means your viewing/search history aren’t recorded, is accessible by tapping your profile icon at the top of the app, then tapping turn on incognito. This makes for a faster toggle than the current search/history toggles, which can be found via library > history > history settings.
The first time you enable incognito mode, YouTube will show a popup, as seen below. The dialogue box warns users that incognito mode doesn’t necessarily make your activity invisible to your workplace, school or ISP.
YouTube’s incognito mode doesn’t keep users signed in, so you can’t use this mode to view age-restricted videos. Instead, the app prompts users to sign in again when playing such a video. The legacy toggles to pause watch/search history are still there, though, so you can enable these instead of entering incognito mode.
In other words, the current incognito mode experience is exactly the same as the one you’d have if you were to sign out in the first place. An easily accessed incognito mode that doesn’t make you sign out would be a smart solution for YouTube — particular as it’s homepage is shown with videos based on viewing history. Check out just one embarrassing clip with your search history active and links to similar videos could be pasted all over next time you open up the app.