Animal Crossing New Horizons offers up a deserted island to build up and call your own. You'll spend all day collecting resources to craft tools and more, though initially you won't be given much inventory space. To increase your pocket space you'll need to purchase a certain item. Info on how to do so can be found below:
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How to Increase Inventory/Pocket Space
In order to increase the number of items you can carry in Animal Crossing New Horizons, you'll need to purchase the Pocket Organization Guide. It will cost you 5000 Nook Miles. Upon purchase, your inventory size will grow and you'll be able to carry more items.
Where to Get the Pocket Organization Guide
The Pocket Organization Guide can be purchased at the Nook Stop in Residential Services. You'll need Nook Miles + in order to buy it. Head here for more info on Nook Miles and the + membership. Once you have the upgraded pocket space, you'll want to start collecting resources like Hardwood and Softwood.