To plant Crops, click the Shop button in the Main Toolbar (bottom menu) and select the Seeds tab.
Choose the Crop you want to grow, then click on an empty plot to plant the seeds. Alternatively, you can click on an empty plot to get to the Seeds tab.
To easily plant more crops after your first one, click and drag over other empty farm plots (with the crop selected). It always helps to check a crop’s harvest time so that you’ll know when to return to the game.