Meditation plays a big part in my life. I have done it almost every day for the past nine months and have done similar stretches in the past. I've also done two longer retreats (10 day vipassana courses), where I put in about 100 hours of meditation each. Through meditation, I learn more and more to let things be as they are, taking an honest look at what is present at that moment, without trying to change it.
Experiencing the benefits of meditation, I am not surprised that many top executives have also found this path to be more at peace. But what are the real benefits of meditation? And how does it work in the brain? Let's first dive into the latter question regarding the nuts and bolts of it.
The neuroscience of meditation
There has been some research into experienced (20+ years) meditators, usually Tibetan monks. What they have found is stunning. The brain waves of the meditators are actually different from people who do not meditate: they show more relaxed brain waves and aren't startled where non-meditators are (loud noises, for example).
They have also put meditators into an fMRI machine and looked at what brain areas are involved. What is striking is that the areas normally associated with the image of self, the relation between self and world or self and others, the so-called Default Mode Network, is downregulated during meditation. This effect is maintained in experienced meditators even when they are not actively meditating. 
What this all means is that meditators learn to be more part of the world than acting opposed to it in a normal subject-object relationship. The feeling of being one with the universe does have a neurological basis. But not only do meditators dampen their ego, because of this they also are more attuned to their subconscious feelings and emotions, becoming more sensitive to tensions. Because of this, they can act in a more compassionate way, not blaming others for their own reactions.
Benefits of meditation
The benefits of regular meditation is well documented. Here are some of the most interesting:
1. Increase in focus, because you learn how to let go of distractions.
2. Better immune response, as one is more relaxed.
3. Lower level of anxiety and/or depression, higher level of well-being.
4. Improved learning, probably due to higher focus.
5. Improved creativity, probably due to filtering the subconscious less than normal.
6. Reduce blood pressure, inflammation, and a bunch of other bodily ailments.
7. Improved empathy and compassion, due to the breaking down of the boundaries of the ego.
8. Higher levels of pain-resistance (although I think resistance is the wrong word).
The beautiful part of it is that they have shown benefits in pretty much every area that they looked, so there are probably many benefits that are as of yet undocumented.
So how to do it?
Sit comfortably, breathe normally, put your awareness on your breath. You could even use the following to guide your breathing:
Just do it for a few minutes a day in the beginning. If you do too much, it might become a hurdle that you are less and less willing to take. Do what you can and build on that.
And remember: when it becomes difficult, it means that it is working. So instead of framing it as difficult, perhaps call it 'interesting'. Happy sitting!