How to buy more land?

You cannot buy more land. You can remove clouds from plots using compasses, as long as you meet the star requirement for each plot. Using diamonds, you can purchase the compasses that you lack in each plot. Occasionally there are sales for compasses using real money.

After you completely open Orchid Island, there are 3 more islands to open, one plot at a time.. Another island will likely be coming soon, but no date has been announced.