Presents

You can only give one present per Sunday. Just make sure you are holding the item you want to give, and go visit the Guardians or Rosalia.

After you are greeted, Angelique says:
That's it, I can give the (item) I have to (whoever) as a present.
Should I give the present?
プレゼントしよっと give the present
やめとこっと stop

After the person thanks you, you go to the regular options for Sunday.

The next day you receive a letter of thanks.

Following that example, don't forget to have the Letter Spirit deliver a letter of thanks after you receive a gift (see also Special Events), it costs nothing and the person will like you better.