There are plenty of projects to do in Animal Crossing: New Horizons and the campsite is something you want to figure out how to unlock early in your game. With a good idea of what to do, it shouldn’t take you too long.
The first thing you need to is to have the upgrade Residents Services building on your island. You can do this by adding five inhabitants to your island, drawing them into your deserted island experience and giving them a new home. They need to be fully moved in, too. After they are all moved in, Tom Nook brings forward an announcement about how the Residents Services tent is becoming a permanent building. You need to wait for it to finish building before you speak to Tom again.
After it’s built, go inside and speak to Tom about the progression of your island. During the discussion, he will provide you with a campsite and all of the required materials you need to place it around your island. To build it, you need to have: 15 pieces of wood, 15 pieces of softwood, 15 pieces of hardwood, and 15 iron nuggets. The iron nuggets may be the hardest material to come by of the lot, but all of it takes time. Once you have all of these materials, return to a crafting station to have it built. The campsite takes a full day to construct.