Simply worded, a sump is just a secondary tank that is set-up and linked into a main / display tank as an option for placing equipment as well as providing filtration for the main tank.
If I have learned anything in this hobby it is that there are many many different ways to achieve a healthy and thriving tank. This could not be any truer with how you choose to set up a sump. Likely the best way to approach this topic is to describe the factors that I learned which go into designing your sump and then show you how I set up my sump just as one example. I hope you will find these sump basics helpful.
When you set out to plumb an aquarium set-up with a sump, the more planning / thought you put into the original set-up, the better it will be in the long run. This is not a very hard thing to do at all, if you focus on the basics and understand them. I tend to think of it in flowing different steps: A) Planning of your flow rates, B) planning the material types and sizes, and C) installation / set-up of the plumbing system. All of what you are about to read below is based on my experiences with various data from some North American manufactures of plumbing products (IPEX, Canplas, and Boshart) which is also detailed in the American Society for Testing and Materials (ASTM) standards.
I will explain what I mean by each step then I will show you examples from one of my reef tanks