There is a photo booth next to your museum on Main Street. You can use it to set a picture for your ID Card. You can even use emotions that Dr. Shrunk has taught you. This page explains how to use it. The Photo Booth is open 24 hours a day, but is closed if your gate is open.
Check on the photo booth next to your museum to go inside. You have to pay 500 bells to go in. After that, there will be a countdown, during which you can tap on any emotions that Dr. Shrunk has taught you. When the countdown reaches the end, the photo booth will take a photo and show you what it looks like. If you're happy with it, say OK, and it will replace your ID Card picture. If you want to try again, choose Try Again, and the countdown will take place again. You can try as many times as you want.
If you want to show an emotion in the photo, just tap an emotion. You can learn emotions from Dr. Shrunk in Club LOL. You can tap the emotion at any time during the countdown, so be sure to time it carefully to get the picture to show the emotion at the right moment. You can try again as many times as you want.
If you want to have a picture with a unique look, hold the L button to make a monochrome picture, or hold the R button to make a sepia picture.