"Mindfulness" is a best-effort translation of the word "Sati". What the word "Sati" really captures is "REMEMBERING to pay attention to what is happening in the mind at all times". A trained mind develops this automatic memory to constantly check and introspect the current state of the mind. Based on whether the current state is wholesome (leading to happiness) the "Sati" helps refocus the mind on wholesome thoughts (this is right effort of noble 8 fold path). Over time two things happen: you get intimately familiar with the workings of the mind and you know how to "manage" your thoughts without using "will" or "force" to repress the thoughts into the subconscious. This is an exercise in finesse rather than force. The gist of it is that "ignorance of reality" (that there is an "I") is the root cause of suffering in living beings. But to grasp that at the "intuitive" level (and not just intellectual) requires years of training and you start to see the fruits along the way.

I used the guided sessions from the free Oak app and a lot of the beginner stuff is about just sitting and focusing on one thing (usually the breath). An early skill is to recognize when a distracting thought enters your mind. You acknowledge it and return to focusing on the breath. I use this when I'm working. If I suddenly remember that I'm supposed to do something later in the week or start to wonder if the SR-71 could ever achieve a trajectory with escape velocity, I write it down and come back to it later.