One of the many fun things about Zoo World is making your Zoo unique to you with customization. Click on the "Visit Zoo" tab at the top of your Zoo (Hint: this tab will always bring you home to your Zoo). If you just purchased items or received gifts in your inventory, the game will ask if you'd like to place the items in your Zoo. At any time, you can click on the Storage icon in your Zoo and that will open up your storage. (Hint: the storage icon looks like a crate and it's next to the shop icon).
Once in your storage, your items are neatly organized by 5 different categories - Animals, Kiosks, Decoration, Maps, and Buildables. To place items from your storage on to your Zoo map, click and drag each item to your desired location. The grid will turn red to indicate where you cannot place items and green when you're in an area where it can be placed. Don't worry too much if you're not sure about how you arrange your animals and items, you can always move things around by clicking on the Storage icon. To edit other islands once you've unlocked them, select the island you want from the bar below your Zoo Dollars. When you are finished editing, click the green checkmark at the right of your storage window and your changes should be saved.