Tap on an empty field to plant crops. A panel will appear above the field showing available plant species and their quantities. Select the desired seed type and drag it to the field. Note that a small amount of your coins is spent on planting each seed. To harvest grown and ripened plants, tap on the sickle icon or swipe the sickle over the fields.
To buy trees, open the Shop (the store icon is located in the lower-left corner) and go to the Plants tab. Then tap on the desired tree and place it on the farm. Tap on a tree with fruit to harvest it.
Learn more about farming and gardening in the Farming section.