To build anything, you need to first tap on the Build Menu button from the main City view.

There are 4 types of Buildings:

Production Buildings
Production Buildings will produce the bulk of your income. In order for them to generate cash, you must assign a Character to these building types. Your Character's characteristics determine what kind of bonuses to Building Defense, Production per Hour, and Production Maximum Capacity your Building will have. But watch out - if you place multiple Production Buildings on the same block, you will attract the police's attention.

Facility Buildings
Placing these buildings on the same block as Production Buildings and/or Real Estate Buildings will boost the Production per Hour and the Production Max. You can place as many Facility Buildings on a same block as you'd like - the only limitation is space.

Real Estate Buildings
These buildings also produce cash, but at slower rate than Production Buildings. No need to assign Characters for Real Estate Buildings.

Defense Buildings
Placing these buildings on the same block as Production Buildings will boost your Production Buildings' Defense, and protect them against Enemy Ransacks. You can place as many Defense Buildings on a same block as you'd like - the only limitation is space.