Instructions
Look for a villager with a gift icon above her head.
Walk up to the villager and press the "LT" button to look at her. This will call up a meter that shows how close she is to giving you the gift. The higher the meter, the better.
Press "Y" to learn more information about the villager, including what she likes or dislikes.
Perform an expression in front of the villager by pressing the "RB" button. Select a category with the directional pad and press "A" to perform it. Categories of expressions include rude, scary, flirty and social. Use what you learn about the villager to determine which expression to perform. If you impress the villager and fill the meter, she will hand over the gift.