Do we consciously, effort-fully try to be present all the time so to evade thinking (which seems impossible), or do we have a mixture of both (don't jump on trains of association - don't fuel thoughts, but also if a thought arises then just watch it with nonjudgment and objectivity and allow it to pass)?
How To Meditate
A lot of it is about attention. Attention is energy. Whatever you give attention to, becomes bigger, and often becomes bigger than it really is. So from early we are just trained to mostly pay attention to what we think, what pops up in our head, and all the attention is going there, making its seem as if thoughts are all that there is...
The "I Am'
All of that is fine. Indeed turbulence can come, thought-storms, even what can feel like physical pain. I see it as the old stuff being ejected, so allow it to all do whatever it wishes. The belief that you are an entity or an object that is a victim or controller of any of these energies is what causes most trouble. Be the "I Am" itself, rather than the attention or sensation that moves in and out of it...