There a a number of different ways that you can set up your home scale aquaponics unit. There is no real right way, however there are a few things to consider to avoid some of the wrong ways. Your choice of system should best suit your needs and resources. One of the first things that you will need to consider is your space requirements and budget. Once you have these two prerequisites worked out you can begin thinking about other things.
Figuring out what type of fish you want to raise and the types of vegetables you want to grow is only a minute part of putting together a good system. You will need to think about tank size verse grow bed size and what type of medium (or soil) will you use? Do you want to have a constant flow system or a ebb and flow system? Can you run your system on solar, or do you want to add a water feature? There are advantages and disadvantages to each system, some out weighing others on a level of personal preference, others on more of a technical level. If you have the option I would recommend trying to experiment with a couple of different systems in an attempt to see what ultimately works out best for you and your environment.
The following is a list of some of the more used aquaponic systems around: