To harvest your plants, they firstly must be fully grown. Remember that some plants will take longer than others to grow and by clicking a plant, you'll see the growth progression.
Once a plant has fully grown, again you'll need to click the plant and then click harvest. Beware that when you harvest some plants, they will not regrow unless you plant more.
There are however, some items that will grow again once harvested. You can find out which plants or items will regrow when you go to the 'Garden Shop' to purchase seeds or items.