Once you've placed a building on any part of the map, you'll earn letters. You can then use those letters to write the names of buildings to later add to your city. For example, you can spell 'flat' to create an apartment building, and then 'garden' to create a park right next to it.
Once you have buildings that provide housing (such as apartment buildings or houses), you'll attract citizens. But once you have citizens, you'll need to create jobs and recreational spaces for them. That means you have to create everything from office buildings and shopping malls to soccer stadiums and tennis courts.
A-B-City's gameplay is much simpler than it might seem at first, which is why it's so much fun. You can spend a nice chunk of time figuring all the types of buildings the game offers, and then even more time trying to make them fit into your city.