It may sound paradoxical, but the deepest sense of reality usually comes from a keen insight into unreality: the varieties of its forms and the underlying structures which give rise to these varieties. Have you ever met someone who you felt had a fascinating grasp of what's going on in the world, an acute sense of reality? Chances are that this person has spent some substantial amount of time and energy in the study of unreality in one or more of its forms. He or she may be a writer or movie director, a dream researcher, a historian, or a business strategist — there are many ways to become involved with unreality. They all have in common that they strengthen your sense of reality in due course.
In part, this has to do with the interplay between reflection and imagination. Reflection, the activity of cutting down instances of unreality when navigating our lives, benefits from a familiarity with all the ways of unreality: the closer you know these, the more successful you'll be in spotting and eliminating them. At the same time, imagination itself is, unsurprisingly, empowered by good knowledge about unreality, and skills in bringing it about. So, for instance, studying narrative structures and writing techniques will help your storytelling (imagination), but also keep you aware of people trying to use them in conversation to appeal to your emotions and sell you something you might not want to buy (reflection); after you've studied scenario creation for a while, you can use the skills thus gained for finding opportunities and threats (imagination), but at the same time they'll help you to recognize and disarm fear fantasies (reflection). And so on.
The dance between reflection and imagination becomes faster and more intense, more high-energy, the more detail and depth there's in your insights into unreality, and that is what increases your command of reality, something that can be felt and seen quite clearly in your interactions.
(In other words, you wouldn't expect a deep sense of reality from people who have a weak imagination, and are 'down to earth'. They might sometimes cut off too high-flying, sentimental dreaming, but tend to live in a boring and impoverished world which is by far not reflecting the whole scope of what there could be for them. On the other hand, people who are too careless and let their imagination roam free without reflection that keeps it at bay are prone to disappointment and miscalculation which lessens their grip on reality and also tends to favor shallow if emotionally intense experience over anything with a deeper and sustained impact.)