Eat is one of the most common first signs. Make the sign whenever you offer food to your baby, when they eat, and just after they have finished. Your baby will be highly motivated to learn this sign, as they will quickly learn that using it enables them to get food whenever they are hungry. As your baby gets more advanced, start introducing the names of specific food items, so along with the general word eat, your baby can start using more specific words like jam, or blueberry.
Eating is one of our favorite signing opportunities. We sign food, we sign more, and we sign all done as part of our meal repertoire.