Yes, you are supposed to put fish in the tank. Not all kinds of fish are suitable, though. For example, some thrive in cold water, others in warm water. Other considerations include availability and legality. You also have to think about the difficulty of maintaining and feeding them and the space they need. All these things and more, you could discuss here.
In 1997, Nelson and Pade started the Aquaponics Journal. For the next 16 years, until 2013, it became the de facto source of news and others related to this incredible growing method. 62 articles published quarterly are available for download. These are invaluable resources that help expand your knowledge of aquaponics horticulture. What better place than to share experiences with others than here?
An aquaponic system is not too different from hydroponics. In fact, it is mainly the same, and you could customize some like drip irrigation, flood and drain, deep culture (water submerged roots), and nutrient film technique. These are all compatible systems, and it would not take too much tweaking. Expert and veteran tips are here to make sure you are on the right track to get things moving in the right direction.
In aquaponics, you feed the fish, letting them provide nutrients through their waste byproducts. It is far much different from the way plants are nourished in soil, hydroponics, or any other growing methods. One of the things you need to do is to provide fish food that does not keep them happy. They should also complement the whole ecosystem, not only the plants but also the beneficial microorganisms. It sounds complicated, but they really are not. And, more importantly, you can find the answers here if ever you get confused.