I saw that it was possible to give gifts to villagers to make them like you so that you could get discounts at the store. How do you do this?
To give gifts you need to find a flower or some other item that they will accept as a gift. Approach them with this item selected and press the action button to gift it to them. You will see an icon of a gift / present above their head if they are willing to accept the item as a gift. Hearts will appear above their head once you give them the gift.
I think the button is X on the PlayStation. Should be whatever button is considered the action button to interact with an item rather than to use it. You might end up eating the item instead of gifting it if you press the wrong one.