This overview shows the typical phases of an open awareness meditation  . This particular generalised structure is in the "modern Dzogchen style"   represented by Sam Harris.   You can generate your own example meditation in this style on any topic here.  

These meditations are secular adaptations of non-dual contemplative practices like Dzogchen and Mahamudra. They are designed to offer direct, experiential insight into the nature of consciousness.

The structure guides the listener/reader from grounding in raw sensory data to observing thoughts as mere appearances. The insight process  culminates in a recognition of awareness as a vast, open space. Space is a core Mahamudra/Dzogchen metaphor for awareness itself, unbounded, unlimited.

These are not concentration-based practices. Instead, their core method uses direct "pointing-out" instructions. Those are inquiry-based questions  or statements that challenge one to find the "self" or observer at the center of  experience. 

The final purpose is to experientially realise the absence of a fixed, separate self ("The not finding is the finding"). If successful, this collapses  the illusion of a subject-object duality. 

Thus, these meditations are far from just trying to generate a calm state, or relaxation.  They would benefit from prior concentration training, in order to follow the instructions and shift in "base of operation" fluidly.  

However, in my experience, the sheer repetition of this kind of meditation will also train the mind if they are a daily practice.  

There are a varieties of teachers in this style. Many or most of them are contributors of guests in Sam Harris´ "Waking Up" app.  Each of them has a slightly different focus.  The application lists a few of them (more could be added, for example James Low).