You'll find the puppet feature under the Puppet option in the main menu.
The puppet will only work while you're in character.
When selected, a puppet prop will appear in front of your hand.
Grab it and squeeze the index trigger to enter puppet mode. Release the index trigger to exit puppet mode and return to first-person control of your character.
Let go of the puppet and it will disappear, but you can always get it again from the main menu.
While puppeteering, your puppet hand controls the position of your character. Your head and free hand continue to control your character's head and other hand as usual, and your lip syncing and facial expressions continue to work as expected too.
You can use your puppetting hand to jump or move around, and the feet will try to mimic walking as you move your character around the set.
You can also pick up and use props while puppeteering, and any props held in your free hand should continue to be held by the puppet and back to your full-body character after you leave puppet mode too.
Next: Stand-ins