Clicking on the plus icon beside your gem resource indicator at the upper left portion of the screen will open up the store. There are several ways to increase your resources via in-app purchase. There are the sale bundles that sells gems with power items or elixir on a discounted price, and then there are the different packages of gems differing in quantity and their price (bigger packages might cost you a bigger chunk of money, but in reality, gems in these packages tends to be cheaper per piece).
Aside from this, you may also purchase access to the 3rd World "Sunstorm Sands", if you are having a hard time completing its pre-requisites. Other than that, there are also the seasonal packages that sells Heroes with spells, or gems.