My personal, limited, understanding:
Right mindfulness is rooted in always feeling the body. This means continuous awareness of sensations in 1) lower abdomen and hips, 2) chest and diaphragm, 3) neck and shoulders, 4) feet.
Mindfulness of body is expressed in your posture and in how you move. Your posture and movements should be royal. This means, relaxed, smooth, precise, elegant, and doubtless. You must always be very comfortable, but not sloppy.
The next component of right mindfulness is simplicity. This means not worrying about too many things. Instead of running around the court chasing the balls, you let reality serve you the ball, and you handle them, while trusting your fundamental sanity.
To add some sophistication to the above, right mindfulness involves changing your frame of reference, from seeing this world as container of people competing for success, to seeing this world as energy, mind, karma. Energy fluctuates and animates, mind receives sensory stimuli, these interact with previous impressions, triggering recognition of objects, these trigger impulses, impulses are dukkha, acting on impulses we seed the seeds that keep the wheel rolling in the same track. So with right mindfulness we have to learn to measure everything with the yardstick of Dharma. We leave the regular world, and immigrate the world of Dharma, where everything looks different and people speak a different language.
As the above is established, the main part of right mindfulness is stalking your ego, stalking your attachments. This involves a very critical, very sincere attitude towards oneself, almost harsh. You watch your mind every second of every minute of every hour for any signs of idolizing anything, making anything all-important: money, success, relationship, respect, spiritual achievement, stability, comfort, fairness, honesty, intelligence, Buddhism -- anything at all. The other side of this is watching your ego for attempts to defend/promote itself. First, you can identify these situations by the negative emotions that arise, and by letting go of attachments watch the emotions subside. Then you will be able to detect the attachments earlier, before emotions arise.
Doing the above, over time you should develop mindfulness of energy in and around you. Is situation balanced or is it skewed. Whenever there is an energy problem, you know you will get in trouble sooner or later. So you learn to maintain your cloud in good shape.
Finally, right mindfulness involves developing the feeling of trust towards your judgement. This trust is based on the fundamental mistrust of your ego, with its tricks and its ability to turn the best Dharma into food for itself. It also is based on simplicity. It is also based on mindfulness of body. It is also based on the dharmic frame of reference. It is also based on awareness of energy. Once all of the above comes together, you know you can trust yourself, which means you can put things on autopilot. You let your fundamental sanity drive. Then right mindfulness becomes effortless, you can't loose it. This is when calm and joy come.