So what do we do during practice? My current understanding

The short answer is that we do two things: 1- We create some space, 2- We look into our mental objects. We shoud first develop some skill about number 1, then having found some skill we can do number 2.
 What dose it mean to create space?
 It means we stop reactivity. It is done by letting go of things in mindfulness meditation and by gratitude and loving kindness practice out of meditation.
 What dose looking into mental objects mean?
 It means we focus on them and investigate the how of them. The natural processes of the mind help us to untangle things gradually.
 So a meditation session has at least two parts, in the first stage we calm down the mind and create some space, then in the second stage we start investigating mental objects, we just look in to them. We do not struggle.
 It is very important not to forget 3 things, we should keep it simple, we shouldn't struggle and we shouldn't be hasty.Right view must also have a role to play here, but it is not so clear for me, so I will write about when I got it!

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Mindfulness meditation, gives us an opportunity to notice the distinction between the sensations and first impressions and what mind builds upon them. Quite often we can let go of some of the secondary mental objects.

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One of the most important teachings of mindfulness meditation is that when emotions arise we can, we really can, stop from getting involved.

Stretching The Space Between Stimulus and Response

Between stimulus and response there is a space. In that space is our power to choose our response. In our response lies our growth and our freedom.

Viktor Frankl

In our everyday life it is not very often to notice how our response to a stimulus arises, however there are times we have the chance to get a rough idea of how this response or parts of it is getting formed gradually, for example some times I can notice how blood runs to my face when I get angry. And there are also times that I have some idea of my intentions when the response is getting created, and in some of these occasions, I feel I have some control over my thoughts and intentions and actions, I feel I can somehow manipulate them to some extent.

Wouldn't it be nice if I could notice this space between stimulus and response more clearly?

Wouldn't it be nice if I could prolong the time I have more control over what I can do?