Animal Crossing New Horizons star fragments are rare and can be found after shooting stars appear. For shooting stars to appear, you need clear skies and a Meteor Shower to appear at night.
Here's the best way to farm Star Fragments.
[Announcement] #AnimalCrossing: New Horizons is now available! We hope to see you traveling to new horizons and enjoying your island getaways! ?️
— Tom Nook (@animalcrossing) March 20, 2020
Animal Crossing New Horizons Star Fragment: How to Farm Star Fragments
So as a Meteor Shower takes place, you will be able to wish on the shooting stars in the sky. However, you need to make sure you're not holding any tools. Also make sure there are no structures or trees blocking the view of the sky. Use the right analog stick to look at the sky.
When the shooting start appears, hit the A button and make a wish. If one of the stars gets larger and brighter, it worked! You can stick around and keep wishing on stars as they keep appearing. After the meteor shower, look around the beach for buried Star Fragments. Every wish made drops Star Fragments.
If there is a meteor shower, Celeste the Owl should around your island. Speak to her and she will give the recipe for a Magic wand.