I've noticed one thing is for certain about this particular style, and that is the lack of information on the topic. Or more specifically, the information that is available on the style is either the same paragraph of information just rephrased or comes from sources that are ambiguous in their language at best for whatever reason. It is my hope that I can shed some light on the topic, and further my learning on this particular area, I consider Iwagumi to be my area of interest, and thus it is of high importance to me to continue a quest to fully understand the style. This quest for knowledge has certainly had many, many doors to go through, half the time each new door being contradictory to the last one, taking jumps from the highly philosophical to the extreme simple.
First and foremost, Iwagumi was not something created or invented by Mr. Amano (although he is rightfully credited for introducing the style into the aquascaping world). Iwagumi is a style that's just about as age old as you can get. Iwagumi (also pronounced ishigumi at times, as far as I know, there is no significant difference between the two pronunciations) in japanese is written as 石組 the first character here means "rock" and the second character essentially means composition, layout, organization, etc, etc. So, an Iwagumi, at it's most basic, basic level is a "rock layout" and nothing more. At the same time, this means both a layout of only stones to create an image or impression, and the method to which stones are placed. So an Iwagumi in aquascaping is a layout composed of only stones, while if you had driftwood in the setup, the stones could be laid out according to "Iwagumi" principles, but wouldn't be an "Iwagumi" lay out as it's come to be known. Essentially it is a style of it's own as well as a subset style part of other 'styles' at the same time. If you ever learn the japanese language, it is choked with contradictory sentiments and words (when viewed from an english native point of view at least) that can add all sorts of fancifully fun confusion (like the word kami that at the same time means hair and god, and the only way (in speech) to distinguish the meaning between the two is the context they're presented in).
Iwagumi is a design principle seen extensively in japanese gardens (which, it really does makes sense that it found its way into planted aquaria), and is probably most readily apparent in karesansui ("zen" rock gardens). The use of Iwagumi in karesansui is probably most likely where the 'classic' iwagumi principles in aquaria resound from (meaning the use of rocks and only one carpet and a single foreground plant), Karesansui incorporates sand instead of water (a very very important concept in japanese garden), using sand to give the impression of water, and has large stones arranged in a specific manner to give certain impressions on the viewer. Contrary to popular belief, sometimes Karesansui's are planted. Albeit typically only with low growing mosses on the rocks themselves (see any parallels here?).
This leads us into the concept of the sanzon iwagumi - sanzon being written like 三尊 where the first character is "three" and the second means revered, valuable, precious, noble, exalted, etc etc, and is often used in compound words that have something to do with the buddha, etc. The idea here is that one main stone is flanked by subordinate stones that 'bow' (literally or figuratively, in the figurative sense they are smaller stones that emphasize the existence of the main stone by 'leading' the eye to the main stone) down to the greatness of the main stone that can come to represent the buddha, god, etc. A sanzon iwagumi can either stand alone in a layout as just 3 stones setup in accordance with this principle, or exist as part of a larger layout (i.e. groups of 3).
Don't think we're done talking about the stones - because we're not through yet! Intrinsic to stone layouts, is also the concept of suiseki 水石 (which uses the kanji's for water and stone). What this is, is basically an art form of appreciation for stones. Stones are positioned accordingly to give certain impressions or create likenesses of something else in the eye of the beholder (an animal, a mountain, a person, etc). The object here is to create a connection with the viewer with the physical object in some manner by reminding them of something / giving a certain impression. What really sends off lightbulbs here is one particular quality - the way in which stones are aesthetically judged here. Deeper colors are more valuable (you know, those deep blacks and grays seen in Seiryu?), deep blacks, reds, greens, etc are all prized. The art here is supposed to be very subtle, impressions are given by very small details of the rocks, its characteristics, things like whether or not a small plant is growing out of a crevice, etc. Signifiers of age are also important (like, quartz veins in the rock). So looking at an entire setup you would end up at the macro level the Iwagumi principles of positioning and creating a layout out of multiple rocks, and then at a micro level the judging of the individual rocks in accordance to suiseki principles. It is not hard to see the multitudes of overlap that occurs in both of these concepts.
An important principle about the individual rock layouts is simply the way the rock is put down. There are supposed to be 10 different views of a single rock that can be obtained by simply turning the rock over on it's side, angling it vertically, etc. Instead of inundating this post with lots of pictures illustrating this idea, i'll simply provide you a link.
Why is this important? Well it works into how to properly utilize your stones to give the impression you want. I commonly hear from people making Iwagumi's that their rocks "suck," which while it can't be said that all stones are equal in appearance, you can improve their appearance by simply tinkering with the rocks position and placement.
A lot of people ask whether or not you have to use a stone like Seiryu or Shou, or Manten to create an Iwagumi layout - this is false. These are only popular stones to be used, in part because of their aesthetic appeal to the japanese. Any kind of stone can be used to create an Iwagumi - you just need to make sure the rocks are the same type or look similar enough in texture, appearance and coloration to appear as to be the same kind. You can easily make an Iwagumi using river rock, pebbles, metamorphic rock, Seiryu, lava rock, etc. In fact, you could apply Iwagumi design principles and layouts to not only freshwater aquaria, but also saltwater and terrarium / vivariums!
The type of stone you pick however, is very important. The type of stone you choose will decide the entire manner of the layout, as well as what plants work better with them and accentuate the stone. Remember the key point here is to accentuate, and emphasis the effect of the stones. This makes stone type, layout and plant selection incredibly important. For example - the texture of hairgrass and hc works extremely well with Shou stone (shou stone is a very vertical and fine type of stone, and the character traits of hairgrass are nearly identical to this, plus the shades of green that hairgrass takes on meshes very well with the texture and coloration of shou stone), however the shape of glosso doesn't really emphasize the stone the same way as it does, say, Seiryu. So not only are we talking about the texture, color, shape and size of the rock, but also the same traits in the plants we choose to plant around the stones!
Sheesh, that was a lot of writing, and I'm probably as tired of writing right now as you are of reading, so I feel this is a good breaking point. I will continue this train of thought later and delve into the actual laying out of the stones, the planting, and all those fun little details.