I wrote this in response to someone I spoke with on IRC who expressed an interest in how grounding and centering works. I'm putting it up here in the hope that it will prove useful to more people this way.
I don't know how familiar you, dear reader, are with the language used for this stuff. There's one caution I'd like to start out with.
There are a number of words with mundane meaning that get used for other meanings, including some with technical meanings in fields such as physics. I use those words here not because I like this (it bothers me a bit, even after this long) but because (a) I don't have any other words and (b) these are probably what you'll run into elsewhere. One of the worst offenders in this respect is "energy". Try to keep it distinct in these senses from any technical meanings you know for it. (Worst offenders, that is, in this piece. The actual worst offender in my experience is "quantum", the use of which almost invariably is based on a severe misunderstanding of quantum physics; even though some of the new-age people try to make it sound as though they're basing their stuff on actual quantum physics, and in a few cases claim that explicitly, to someone who does know something of the physics, all they're doing is revealing how little they know of it. I still haven't figured out even a good guess at what, if anything, they're talking about when they throw around the term.)
Grounding-and-centering is a technique commonly (in my impression) used in neo-pagan circles before pretty much any kind of working. It's also used in the new-age world, but (again, this is just my impression) both the name and the thing are less common there. (I think this is unfortunate and may be related to the new-age reputation for having looney-tunes characters running around in it. Doing energy work or magick when not properly grounded is likely to cause both the worker(s) and the working to go a bit loopy; doing so routinely is likely to lead to, well, routine loopiness.)
While I do believe there is an underlying reality behind this stuff, I make no pretense of knowing what it is, if indeed there is any "what" that human minds can work effectively with. The descriptions I use are just the ones that work for me (or in some cases for others, as described below). If you have something different that works better for you (whether you come up with it yourself or get it from elsewhere), go with it. Much of the reality, if any, here is far more subjective than mundane reality is.
So.
Think of yourself as having multiple bodies. (I don't know how many there are, if indeed they're distinct enough from one another that counting them is an applicable concept. But this is a useful approximation in some respects.)
For my purposes here, I'll simplify it to the point of saying we each have two bodies, a physical body and an energy body. The physical body is the one we generally think of as `our body', the one that is essentially a hugely complex mess of interlocking chemical machinery. The energy body, in this simplification, includes everything else. The energy body, in most people, most of the time, more or less overlaps with the physical body, though its spatial extent is less well defined. (How the bodies affect one another is a question I'm not going to address here; that calls for a whole essay of its own.) The energy body, in particular, is far more protean than the physical body, much more amenable to extension, contraction, and reshaping, needing little if anything more than will to do so.
Grounding and centering amounts to extending one's energy body to what I'll call `grounds' and exchanging energy with them, bringing one's intent and awareness back to one's centre, which typically is somewhere around the centre of gravity of one's physical body (which is, for most people, a little above the navel and about midway between the front and back surfaces at that point), or a bit higher, around the heart chakra.
I call them `grounds' mostly by analogy to electrical grounds, though the analogy is far from perfect. In particular, energetic grounds can both source and sink energy, depending on the energy and the intent.
What you think of your grounds as being is one of those things that is very person-dependent. When I first encountered this stuff, it was in a neo-pagan religious context, in a tradition that used something they called the Triple Centre, made up of the Well, the Fire, and the Tree. This was first taught to me in the context of opening a ritual, and the person who was leading would typically instruct us to reach down to the Water, up to the Fire, and see ourselves as becoming the Tree linking the Water, the Fire, and the Middle Lands together. (Those of you who have Norse mythology knowledge may recognize Yggdrasil lurking here.)
Thus, I found myself reaching down to the primal Water, up to the primal Fire, and drawing them both into myself—or ourselves, when in ritual with others—midway between them. I didn't realize what I was doing was a ground-and-center until I sketched it to a few people and they spoke of it as grounding, remarking that it automatically left me centered as well.
When I got involved in new-age ways, I came to see this as, instead, reaching down to Mother Earth and up to Father Sun, drawing holy white fire from Mother Earth and holy golden fire from Father Sun into myself, flooding myself with those energies, washing out anything stagnant or otherwise impeding me. As sketched above, I'm not convinced there is any real underlying difference between these two ways of looking at it.
I have met at least one person who has trouble with descriptions like the above and who finds it easy to ground by seeing the energies as electrical and the reaching to the grounds as extending an electrically conductive rod. Once again, this is more a question of what images your mind can use to ground effectively than it is a question of which images are right and which are wrong. There is no objective right and wrong here, only a subjective right and wrong, only which images work well or poorly for the person under consideration.
One other note: for practical purposes, the grounds hold an unlimited supply of these energies. I don't know whether the supply is actually unlimited or there simply is a limit so large that it amounts to the same thing in practice, or perhaps this is another question that doesn't have an objectively correct answer.
That's the theory. But, like a lot of other skills, nothing can make you good at this but practice. I can't give you practice. But I can give you a sample guidance script. This is the kind of thing I might speak when guiding people through a ground-and-center for, for example, a journey meditation. The wording here is a bit of a cross between the Water-and-Fire I started with and the Earth-and-Sun I have found myself drifting towards; as I mentioned above, there is nothing inherently right about this. It's just what works for me. If you have some other imagery that works better for you, try using it instead.
My wording here is also a bit abbreviated, as compared to what I would actually say. For example, the "reach down" paragraph here would take maybe 15 seconds to read out loud. I would probably repeat fragments of it and ad-lib similar wordings to extend it to a least a minute or two.
Sit comfortably, feet flat on the floor, hands palms up on your thighs.
See yourself as a tree. Let your roots grow down, down from the base of your spine, down from the soles of your feet, down, down, past the floor, past the soil and plant roots, reaching, down, down, past the bones of long-dead creatures, past the bedrock of the planet, reaching down, down, down, to the centre of the Earth.
See the heart of the Earth as a great quartz cluster, the size of a small house, glowing with a holy white fire. Grow your roots, wrapping them around the quartz, covering it completely.
Draw that white fire up, up through your roots, up past the rock, past the soil, back up to your earth star, up further, rising all the way up into your heart centre.
See it flooding throughout your body. Let it remind you you are made of light. Draw on that light and flood it through every crevice and cranny of your body until your body is filled with light.
Extend now up, like the branches of a tree, up out your crown, up to your soul star. Continue up, up, like the branches of a tree reaching for the sky. Grow up, up, up, until you reach the golden fire of the energy sun above us, never mind where the physical sun is. Feel that holy golden fire on your leaves and branches. Let your branches grow around the sun, soaking up that golden radiance.
Draw that golden light down through your leaves, your twigs, your branches, down the trunk of the tree, down, down to your soul star, down to your crown, down into your heart. Feel the holy golden fire from Father Sun mixing with the holy white fire from Mother Earth. Flood them both throughout your being, throughout all your selves, here or elsewhere; past, present, or future; this timeline or any other. Or, as I like to say: anywhere, anywhen, anyhow. Let the white and gold fires fill you with love, flushing out any stuck energy or emotions that are holding you back from achieving your highest purpose this life. Surround yourself with the holy violet flame of the Cosmic Corrector, of Saint Germain's Fire. Let it transmute anything flushed out, transmute it to the pink fire of pure love.
Feel the golden fire running down through you into the Earth, the white fire running up through you into the Sun. Center yourself in your heart chakra, feeling the gold and white fires running through you, flooding your being. Surround yourself with the holy cobalt-blue light of Archangels Faith and Michael and know that you are protected from malign influences.
And then you do whatever you choose to do next. You could return your awareness to the mundane and resume your day from a point of greater calm. By this point you are probably in a light trance; you could move into a deeper meditation. You could proceed to a psychic journey, if you have anywhere you want to go. You could just contemplate the experience to see what you can learn from it. You could practice a psychic skill such as psychometry or remote viewing. You could pause, as still as you can manage, to listen for any messages Spirit might have for you. You could draw on more energy and, for example, start raising a cone of power for a magical working. There are many options; these are just the handful that occur to me offhand.