Landings seem to be recorded almost no matter what you do. Even landing in places where there isn’t at airstrip. I used to think the landings required ATC interaction, and perhaps it was, but it isn’t now. If I conduct a flight, and opt not to use ATC, I might see a single takeoff, and 22 landings, during a bush flight trip for example.
For the takeoffs to register, ATC interaction is needed. At a controlled airfield, this is easy. Contact tower/ground, request takeoff/taxi, hold short, request takeoff, job done. At an uncontrolled field, first request taxi, if you have assists on follow the markers to the runway, then announce takeoff. That should log the takeoff.
What really seems to drive it all is what’s in the pop-up “Objectives” window. It indicates what the sim is expecting you to do next. In the example of the uncontrolled field, in the ATC dialogue, if you don’t request taxi first, and instead announce takeoff, I don’t believe it will log your take off. Taxi is requires first, and you will see this will nudge the “Objectives” window along to the next stage.
I made a post describing these various stages, from startup to shutdown, some time ago. I have since noticed some different objectives stages that sometimes pop up so the list below is not exhaustive.