To gain a general understanding of the workings of a sump system, you can do no better than read
this article. As for how to use a sump to provide filtration for your tank, there are a million ways to do that. Today most people who use a sump will install a wet/dry system in it. That kind of setup is so popular that many newcomers think the terms 'sump' and 'wet/dry system' are synonymous. In a wet/dry sump water trickles over various layers of media until it reaches a reservoir at the bottom of the sump, from where it is pumped back into the tank.
There are many advantages of a wet dry system, the main one being that the bacteria can directly draw oxygen from the air. In my opinion that's a non issue, because if you are using a Durso type drainpipe oxygen levels in your water will be at saturation levels, and the bacteria will get more than enough oxygen out of the water. The main disadvantage of a wet/dry system are that the sump can not be filled all the way with water. This means valuable system volume is wasted. In addition, the tricking water produces quite a bit of noise, making such a system considerably louder than a good canister filter.
In the
sump design I am using for my 240G, the bacteria can only draw oxygen out of the water, meaning it is not a wet dry. That allows the sump to be filled with water as far as possible. You need to have some spare capacity for water that rushes into the sump when the pumps are turned off, but that's another story. At any rate, the design I am using maximizes total system volume, and is as quiet as an Eheim 2260.
It consists of a simple sheet of Poret Filter Foam that sits in the sump container as a divider. The drainpipe releases water into the sump on one end, and the water needs to flow through the foam sheet before a pump on the other side picks it up, and returns it to the tank. Since the foam will take on the shape of any container, irregularly shaped sump containers like cheap plastic totes can be used. There is no need to install baffles. For my 240G I am using two 45G plastic totes, adding a whopping 90G to the system. Each tote has one Poret Foam divider, making for a total of two approximately 2'x2' sheets. Even with a heavy stocking level in a tank of this size, I don't need to clean the sheets more than twice per year, and they provide the entire bio and mechanical filtration for the tank. There is no need for bioballs, filter floss, carbon, or any other additional filter media.
Because my sumps are a tight fit in the cabinet and there are two of them, the process of draining them, taking them out of the cabinet, cleaning the whole mess, re-installing everything, and filling it back up with water takes me almost half a day.