There are 2 storage buildings, the Warehouse that holds all your Edibles and Buds, and the Shed, the building right behind the Warehouse, which holds all your upgrade items.
An image of the Warehouse screen.
If you find your Shed or Warehouse is full and you are unable to pick up more items, you can delete items using the trash can button, or sell them using your Dispensary. Selling items in your Dispensary will free up space in your Shed and Warehouse, as well as earn you a tidy profit.
An image of the Dispensary, filled with Chocolate, each priced at 420 bucks.
If you sell things in the Dispensary regularly, then you can efficiently manage the capacity of your storage. You can also use the extra cash to buy materials needed to upgrade your storage, which will make inventory management even easier. This also ensures that later in the game when people are using the Global Market, it will stay nice and stocked with a variety of items for players to buy.

Another way to clear out some extra inventory is to complete deals at the Weed on Wheels. You can hit the blue recycle button to cycle deals and, after a short cool down, get new deals that might need buds you already have.

Alternatively you can try and upgrade your storage for more capacity. You can do this by tapping on the Shed or Warehouse, and then the “increase storage” button. A pop-up will show you what items you need.