There are two kinds of houses in Skyrim - the houses you can buy in the base game, and the houses added in the Hearthfire DLC.
The houses that you can buy that are directly in a city are part of the base game. This includes the house you bought in Riften. The customization options in these houses are limited, basically just adding or removing furniture.
There are three plots for houses that were added in Hearthfire. In order to purchase a plot, you'll need to become a Thane in that region. For Falkreach, this means doing some quests for the Jarl. See the Elder Scrolls Wiki for more details.
You should be able to build a crafting bench for your house once you unlock the plot and build a few rooms.