Here's a link to one of the better vids I can find on the workings of an airlift. A bit lengthy, but should leave few questions unanswered. These things clearly have a lot of applications. Most of us likely have the parts needed kicking around the house already, so not a lot of effort to slap one together & see how it works.
https://youtu.be/_j0tmCc5Z3Y
In essence, the construction is similar to an air stone skimmer. Micro bubbles in the skimmer pick up organics & transport them to the surface, the air lift uses larger bubbles to bring water to the surface more effectively. The elbow at the top either discharges the water back into the container, or out, depending on the application. I wonder if a venturi part way up the riser pipe would improve lift efficiency.... a patent in the making??
Here's my skimmer, shows the rigid airline inside the skimmer body, same idea for my version of the airlift:
