On this page of our guide to Animal Crossing New Horizons we describe how to shoot down a gift that flies over the island.
From time to time you will hear the sound of a strong wind. If you look up at the sky at that moment, you'll probably notice a gift attached to the balloon. The package is calmly flying over the island. How do I get it?
You'll need a slingshot to get to the package. You can find the DIY recipe in the store of Nook Brothers. It should be available during the first week of the game - if it's not there, you'll have to make some progress in the main story (if you don't know what to do, talk to Tom Nook at Resident Services).
Once you've made your slingshot, it's very simple. Stand roughly towards the gift and use A button to shoot towards the balloon. If you miss it, then it's a good idea to change your position. After some time, you'll learn how to knock off gifts with a single shot.
Note - Remember to check the position of the balloon, before you start shooting. If the gift is flying over the river, sea or a lake then you will lose its content. You'll get a few Nook Miles as a reward. ;)