Obviously the central point in creating a city is to build, build, and then build some more. You can buy new buildings from the 'Build' menu, accessible through the button in the bottom right-hand corner. Here, you can select houses, communal buildings, decorations and businesses to build. Pick a category and then select the building you wish to buy. Some buildings are locked until you have levelled up sufficiently, added enough Neighbors, or completed certain other goals. There are a few of these which you can only buy with City Cash, to try and give them an exclusive feeling.
Once the purchase has been made, you can select a plot of land on which to place the building. It is important to try and make sure they are on roads so that people can access them.