To get your villagers pictures, you need to become best friends with them. To become best friends with another villager, you need to talk to them a lot, do favours for them, go to their house sometimes, invite them over to your house sometimes and never hit them with a net or a eekhammer.

The second way you can get your villagers pictures is when it's April Fools on ACNL, if you pick the fake copy of the animal, the real one will give you their picture. You can get all of your villagers pictures if you pick every fake one correct.