Whenever you acquire a dragon, a cave card, or a resource, by default that item goes into your hand or your personal supply. Some dragons allow you to acquire an item and also provide optional secondary abilities, such as caching a resource or tucking a card. If you decline to do so, that item remains in your hand or your supply.
For example, see the Beckoning Cricketcatcher to the right. At the end of each round, you gain 1 card (from the face-up display or from the deck). After looking at it, decide whether to keep it in your hand or to tuck it under any dragon. If you tuck this card under a hatchling with a “tuck” ability, gain the benefit provided by that hatchling.