From your island home screen, tap on the Shop icon displayed on the bottom banner. You will see an array of categories from which to select. Within each option is a list of items and their cost. If the cost is in red, that indicates you do not have enough currency to purchase. Once you buy an item, you will be directed back to your island in order to select an available location (indicated with a white dot) to build/plant your new item.
Certain items require more space, as indicated by the available locations. If you have a lot of plants/buildings, you might need to move/sell items to make room for more. Reference the following article for more info regarding this: http://support.striiv.com/support/solutions/articles/79745
Each item you buy has to be grown or built AFTER its purchase. This is done with the energy points you earn from walking and moving.
The amount of energy needed and the amount of coins earned differs from item to item. Once the item is completely grown or built, tapping on the item and tapping once more will pull up a Details screen that indicates how many coins/gems you will earn.