Vedanta traditionally recommends yogic meditation as a preliminary discipline to help prepare the seeker for Self-inquiry. For this, it's often suggested that one follow the instructions outlined in Patanjali's eight-limb path (sometimes referred to as ashtanga yoga). However, within the Vedanta tradition, sitting meditation can also be used as a method for internalizing the knowledge once it's learned (nididhyasana, the last phase of Self-inquiry).
It should be emphasized that Vedantic meditation isn't for gaining knowledge or removing doubt; for that, you still need the other two phases of Self-inquiry practice, shravana (listening to the teachings) and manana (clarifying). That said, Vedantic meditation really just boils down to dwelling on the thought "I am Brahman (pure awareness)." This doesn't necessarily need to be done while in a sitting position. It can be done anytime. Walking alone in nature is a great opportunity to dwell on such thoughts.
Because the following meditation works through the heart, it helps counter the argument that Vedanta is strictly an intellectual exercise. In fact, when properly applied, Vedanta is personality-changing, leading to a whole new outlook on our experience.
The instructions below describe the method for reaching a Vedantic meditative absorption (samadhi), which is not experience-based (dependent on having a special experience such as nirvikalpa samadhi) but knowledge-based (dependent on learning and understanding the teachings as taught by a qualified teacher). The following instruction mixes both traditional yogic instruction for settling the mind with Vedantic meditation/contemplation.
Find a quiet and clean place to sit. The best time to meditate is in the early morning before the day leaves traces on the mind that we can become attached to. Think of meditation as a temporary respite from the world. Meditation done properly is like taking a vacation from samsara.
Sit comfortably on the floor or in a chair, and in a position that allows you to keep still for several minutes. Put your mind and body on notice that it's not nap time by sitting with a straight back, neither too relaxed, nor too rigid. One should be comfortable but attentive.
Remember to not take meditation practice too seriously. There should be a certain lightness to your approach, absent of any tension. Meditation is best approached with the karma yoga attitude, which means that whatever happens as a result of meditating (joy, peace, contentment, insight) is not up to you. Meditation isn’t about controlling the mind but rather, setting up the right conditions so the mind can become sattvic. Once this is achieved, our job is to get out of the way. Vedanta meditation, in particular, isn’t about having any kind of “enlightenment experience.” You already are that which you seek, any joyful experience is just a reflection of the Self.
Root yourself in the body by watching the breath and at the same time relaxing the body. It’s not particularly important where you watch the breath. It can be at the tip of the nose or simply watching the rise and fall of the abdomen. Stay there until both body and mind feel relaxed and concentration has developed.
Now, firmly establish yourself in the thought: "I am not the body, I am the witness of the body. I am not these thoughts, I am the witness of these thoughts." Create space between the subject (the Self) and any objects that appear on the screen of consciousness. (Note: Unlike traditional yogic meditation, the goal of Vedantic meditation isn't to reach a thoughtless state. In Vedantic meditation, the thought is the object of meditation. This deliberate effort to bring the mind to a Vedantic thought is called dhyana.)
Next, start with a phrase that describes the Self such as, "I am whole,” reciting it slowly and with sincerity. Repeat it a few times until you are able to feel it in the heart-center. When the feeling evoked by the phrase begins to fade, try another phrase repeating it slowly and deliberately, such as "I am eternal.” Likewise, do the same for one or two more phrases using a different word to describe the Self. Repeat the cycle of phrases if needed, or just stick with one until it resonates. Another way is to start with a few phrases and then afterward, just repeat the word describing the Self, letting it slowly sink in: “whole,” “eternal,” “limitless,” “infinite,” etc. Before long, the words will begin to quietly echo based on their own momentum without any effort on your part. This effortless concentration is referred to as samadhi.
Other phrases you might try:
I am whole…complete…limitless…unchanging
I am the light…formless…eternal…all-pervading
I am that which is beyond pain…old age…sickness…death
I am that which is beyond birth…death…space…time
I am pure...immutable…happiness…peace
Continue until there's a feeling of resonance in the mind and throughout the body. This feeling of wholeness and limitlessness is now your object of meditation.
Observe any tension created by thoughts that appear and distract you from the object of meditation. Don't push thoughts away. Instead, welcome them, but don't feed them. Take a subjective view knowing they aren’t you. Give them space and observe how they rise and fall of their own accord.
Distractions are simply a reflection of likes and dislikes. Don't pay attention to their content or try to analyze them. Only observe the mechanics of their coming and going. By not paying attention to a thought, it will lose energy and pass away of its own accord.
Pay attention to any hindrances to your meditation in the form of the gunas.
Rajas = desire, anger, or restlessness
Tamas = dullness, sleepiness, or doubt
Refrain from liking or disliking any hindrance. With nonjudgmental observation, view the hindrance as just another object on the screen of awareness. Notice how it shows up through any one of the sense doors (sight, sound, odor, taste, touch or thought). Observe how likes and dislikes create a subtle tightening sensation in the mind and in the physical brain.
Manage any distractions or hindrances using “the 4 R’s”:
Recognize that the mind has drifted away from the object of meditation
Release attachment to the sensation or thought
Relax into any tension felt in the body or mind
Return gently to the object of meditation (e.g. "I am whole, complete, non-dual awareness")
Feel the rise and fall of any tension as likes and dislikes, memories, emotions and thoughts come and go. Make sure to relax again after the release of a thought so that the mind begins to regularly settle back into a state of calm and ease.
As in ordinary life, sometimes unwholesome states arise during meditation.
Observe that an unwholesome state has risen
Refrain from giving the unwholesome feeling more attention, but don't try to push it away or control it either
Replace it with a wholesome feeling (e.g. "I am whole, complete, limitless non-dual awareness.")
Stay with that wholesome feeling
Once the mind has quieted and joy has arisen from the object of meditation, stop any verbalization and just appreciate the peace and sense of contentment (sattva) that was cultivated. Thoughts may still arise but their staying power is now weak and only appear as blips on the screen of awareness. However, if thoughts do become a problem again, re-establish yourself in the body and apply the 4 R's (recognize, release, relax, return).
Resting in Awareness as Awareness
In the final phase of meditation, all internal verbalization has stopped along with any tension generated from likes and dislikes. This phase is marked by peace and collectedness. Expand your attention to include the space, silence and stillness that surrounds you. Let your body fall away and merge with a feeling of expansion.
Lastly, turn your attention away from the object of meditation and turn it toward that which is aware of the object. Rest in this bare awareness which is a reflection of the Self.