To add more empty plots to your farm, click on the rake and move icon in the Main Toolbar (bottom menu) to open the Tools bar.
From the sliding menu, select the Plow tool.
Then, simply click on an empty area of your farm to add a new plot.
If you’re curious about how many plots you have on your farm, click on the Mastery, Achievements & Collections button (ribbon icon) in the bottom menu, then choose the Mastery tab.