There are two ways to obtain more expansions in the game. Each expansion adds a new 5x5 grid to your city. You can obtain them by clearing provinces on the world map, from the research tree, or by purchasing them. There is an expansion tab under the builder icon in your city (bottom left). When you click on that, you'll see the option to buy diamond-enhanced expansions listed under premium expansions. (You don't have to buy them, but doing so immediately expands your city.)