I have tried to make these instructions agnostic/tradition-neutral. I think that every human being is capable of exploring their own mind. These instructions are based on my experience(s).
I will give you the instructions all at once, because, if you do it correctly, my voice (or this text) should become harder and harder to hear (or read), the farther you go. Also, you would be going below the level of discursive thinking in your mind, and human language seems to be limited to the discursive level.
If you have any duties that require constant attention (e.g., young children, a serious health problem, etc.), make sure someone else is monitoring them, because you may not be available. Sit upright in a quiet place with dim lighting, which is neither too comfortable nor too uncomfortable, and close your eyes. Nothing else matters as much as what you are doing now. If the phone rings, if you hear someone speak, if a dog barks, if a car passes, if a lawnmower runs, if you feel a pain or an itch in your body… ignore them. Push the world away, and go into the darkness of your mind. It may take 15-30 minutes to adjust to that feeling. Just ignore the time and focus on going into your mind. If you have trouble ignoring the world, create the image, no matter how vague/blurry, of a pole, a line, or something else that is simple and stationary, in the middle of your mental field of vision, and focus on that to the exclusion of everything else.
Eventually, you should start seeing mental images, like a lucid dream. Watch them, but keep them at a distance. Don’t give them any encouragement or energy. Don’t get attached to them or emotional about them; if you do, you may have a hard time going any deeper into your mind. Notice how they come and go on their own, if you do not interfere with them. That is how the mind works: one momentary construction after another, in an endless series.
After a while of watching mental images, apply your mental focus/energy to push them away like you did ‘external’ sensations, and go deeper. Gradually, the mind should feel brighter and brighter, like someone is slowly raising the light level in the room. If you were to open your eyes at this point, the room might actually feel darker than your mind just felt. Continue applying your focus, as the mind feels brighter and brighter.
You might see a vision, at this point, such as that you are flying atop an infinite expanse of clouds. Whatever you see, you can explore it, but do not get attached to it or emotional about it, or you may not be able to go deeper. Wherever the light or brightness is in the vision, work on approaching that brightness, which usually requires steadily increasing focus and effort.
If you believe in a religious tradition, or perhaps even if you are just in a religious place (e.g., a church, mosque, temple, vihara, etc.), you might experience a religious vision at this point. You might see one or more religious figure(s) (e.g., a Buddha or Bodhisattva; Christ, Muhammad, or an angel; a Hindu deity; etc.), which might be more beautiful than anything you have ever seen in the world, and more and more mental focus might be required in order to approach them. You can choose either to work on approaching them or to work on going towards the light/brightness, which may be different/separate than approaching the religious figure(s). If it is too difficult, slow down and rest, or stop the meditation (see the next paragraph, for instructions on how to stop) and try again later. These beings/things are always there, available to you. If you are able to reach the religious figure(s), you might be able to have some interaction with them and maybe learn something from them.
To stop meditating, it is best to slowly return back up through the things you have been holding back through concentration. If you suddenly stop concentrating/focusing on holding them back, they might all come rushing back, like flood waters after a dam is broken, which can be unpleasant. Whether you stop slowly or quickly, you might feel unusually strong cravings for worldly things (entertainments, food, sex, etc.) as well as anxiety or depression about returning from a more heavenly place to our more stressful world. But you also should have a deeply peaceful feeling and memories about what you experienced while meditating. Finally, depending on how deeply you have gone into your mind, if you stop meditating suddenly, you might return to a sleeping state, instead of to a conscious state.
If you ignore any visions and continue towards the light/brightness, you should eventually begin to experience the Jhāna process, which progresses through a predictable series of signs and stages that are known to several Dharmic religions. The stages are characterized by the mental light becoming brighter and whiter, and the feelings at each stage becoming more and more refined/subtle forms of a peaceful happiness. Eventually, Theravada Buddhists think, one realizes that the mind’s nature/core is always brightly radiant and in a deep state of peaceful happiness, but that it becomes harder to see the brightness the farther away from the core one goes, the more involved in worldly constructions one becomes. At the last stage of Jhāna, according to early/Theravada Buddhism, one supposedly can see that there is a better, more stable/permanent state of being in which the mind can live (called nirvana/nibbana), and that it is possible to transition from our current state (called samsara) to that state. One who completes that transition is said to be Enlightened, an Arahant, one who will not be born again into any impermanent world.
Whatever path you choose, be patient with yourself and don’t give up. May you always meet with spiritual success.