It's an old yoga story, about the onion. We keep peeling off the layers that are not-self, first the body, the emotions, mental, etc. until we arrive at what can't be peeled away. There's a bit of difference between Vedic and Buddhist conclusions about what you're left with, and different practices, and specifically highly different meditation practices. In yoga the body and mind are transcended, a full state of trance is practiced. In Buddhist mindful-based practices, stillness and mindfulness are considered to be more effective.
If you look at the Anapanasati Sutta, you do your mindful breathing, conscious of the depth and duration of inhalation and exhalation. Then we learn to do that within Four Foundations/Frames of Reference/of Mindfulness - body, feelings (perceptual sensations), the mind itself, then mental qualities - and then exercise in this manner to traverse the Seven Factors of Awakening/Enlightenment. Now, for a student who has looked deeply into the Seven Factors of Awakening it's unavoidable to see the over-lap with the Jhana factors. However, simply falling into a mindless serenity "trap" or going off on and endless Jhana "trip" we work through the 7 Factors - steadiness of mind (piiti), comprehension and discernment (dhamma vicaya), persistence/energy (viriya), rapture/mindfulness (sati), serenity (passadhi), concentration (samadhi - yes we do samadhi!!) , equanimity (uppekha). It's better not try try to analyze this too deeply, because it's the direct experience you need more so than the mental knowledge of it. I'm looking at Thanissano's translation. http://www.accesstoinsight.org/tipitaka ... .than.html
In this way stillness of mind is achieved. But in and of itself, it's not awakening. Still, it's necessary.
It's almost better not knowing the details because there is so much confusion about jhanas, vippasana, etc. What you do is sit and get started. If anything, use equanimity as a goal rather than samadhi. Samadhi can become another bottomless pit.
Going more deeply into it, we work with the Foundations of Mindfulness/Frames of Reference vis-a-is the Maha-satipatthana Sutta http://www.accesstoinsight.org/tipitaka ... .than.html
- then also the Seven Factors of Enlightenment see http://en.wikipedia.org/wiki/Seven_Fact ... ightenment
Warning: there are controversies and discussions about some of the key-words used in this post. My emphasis here is don't think about it, just do it.
Also please compare translations - they differ.
- h a n s e n -
p.s. Stream Entry usually happens when uppekha can be sustained during sitting practice. Just start doing it, it will all sneak up on you.