Early on she mentions Thich Nhat Hanh; if I had a "guru" when I was deep in Buddhism, it was certainly him. I loved his books, sought his dharma talks, and followed the goings-on at his Plum Village retreat in France. There actually was a Buddhist temple in home town, which I enjoyed going by but would never have considered going in—theirs was a cultural emphasis, and my interest was solely on the 'dhamma'.
My memory of Thich Naht Hanh's mindfulness is best represented by the dish-washing she mentions on the podcast. When you're washing the dishes, you're not thinking about Cicero's De Finibus; you're not thinking about work, or an interesting podcast. You're not listening to an audiobook—you're really not even thinking about the dishes! Your whole attention is trained on to the motions, sensations, the experience of dishwasher.
A thought will arise; you will acknowledge it, and then let it go. There will follow a moment of mental 'blankness', but inevitably, another thought will arise.
You will acknowledge it, and let it go. Your project is to clear your mind of the whole process of cognition. Your mind does not want to be clear—it has aeons of natural selection and a whole lifetime of habit driving it toward this singular purpose—it wants to think! But you are going for mindfulness, so you clear it again. You are trying to be in the present, fully awake to experience and sensation, but not to thought. Thought is a distraction from the present moment, and you are trying to be present.
Here's the thing; after a few thousand hours, or tens of thousands of hours, this training will result in a few empirically verifiable changes in the brain. The brains of long-practicing monks look different under brain imaging scans, and function differently; they've aged better, have more activation in the "good" areas (happiness, altruism) and less activation in the "bad" areas (fear, selfishness, anxiety).
Mindfulness in the early attempts can be really frustrating, and most people give up. In some individuals, where the mind is especially troubled, mindfulness can exacerbate existing mental health problems. But the biggest problem for me is the discipline required, and the colossal time-sink involved.
Personally, I got to a point where I chose to rely on the hope that there exist other pathways to happiness, and I abandoned that one. I'll never have the brain of a master meditator; but I like to think I've still got a fair crack at long-term happiness.
But you know what? For the sake of experiment, I may give it another try!