They have 5-fold radial symmetry, with 5 red eyes on 5 eye stalks. Their bodies are cactus like, with protrusions and recessed ridges. Within the 5 recesses on their vertical body trunk, there are 5 collapsable membranous wings. Each section of the "head" has a breathing and eating organ, each ridge on the body has a branched "chroinoid like" stalk which branches into inermberable tiny fillament like fingers. The ridges then come away from the body at the base, forming 5 large ambulating tentacles, at the end of each is a large triangular flipper.
They are intensely intelligent, literate, and communicate through a (presumably) pentatonic musical phrase based language by "Piping" through their breathing organs. Their language resembles are series of dots in 5-themed patterns on a musical scale, IIRC.
They are technologically advanced (Or, were in the past), and are capable of using tools. They are far more intelligent than your average elf. They do not ascribe to silly notions of magical harmony like elves do, and follow instead something similar to "Manifest Destiny". They have no qualms at all about creating and using slaves. (Yes, creating. In Mountains of Madness, it is stated that the Elder Things are responsible for the creation of life on earth, specifically to sate their hunger and desire for conquest. They fatten up on worlds they conquer, then fly up into space, and across the interstellar void. They sustain themselves in transit with their photosynthetic abilities.)
We can dismiss with much of the above, and settle for the "Degenerate form" described in mountains of madness instead. This removes most of the issue with alien technology and space flying-- but still leaves the OM NOM NOM NOM and "Do my work for me SLAVE!" features.
Basically, in the story, the protagonist discovers a lost enclave of these creatures that survived the ages by being encased in a primordial glacier as the continent of antarctica moved to the southern polar region. This was the capital city of the Elder Things, and was on the surface. When initially constructed, it was on the super-landmass of pangea, but as techtonic forces split the landmass apart, it moved into less and less habitable climates. The Elder Things are theoretically immortal, so the concept of geological time is moot to them. When they arrived on earth, it was completely lifeless. To satisfy their desire for eating meat, they created simple biotic life and introduced it into the oceans, where it then evolved. At the same time, they created their servitor species, the Shoggoth, which are essentially "Humongous" versions of single celled life.
The shoggoth were created as slave labor, but were endowed with a simple intelligence so that they could understand and obey the directives of their creators. This period represents the "Pinnacle" of elder thing history where they had profound technological mastery, and still were able to take to space at a whim. However, the shoggoth evolved very quickly, and developed more sophisticated intelligence, and a sense of individual will. In the intermediate early decline, the shoggoth rose up against the elder things numerous times and were always defeated, by increasingly sophisticated technology and weapons. As the shoggoth got smarter, the Elder Things got dumber, however. Not using their abilities, they atrophied to where they could no longer fly into space. They also relied more and more on the shoggoth to create public monuments and large art installations, and their artistic skills declined as well.
By the time Antarctica was getting the deep-freeze for the very first time, the Elder Things had reached the late decline and degenerate state that our protagonist finds them in. Seeking to escape the coming permanent freeze until the continental drift pushed the continent back into temperate climates again, they excavated deep underground where geological heat sources enable continued survival. Not all were able to go into the shelter however, and many were left to become little 5 tentacled popcicles on the surface. The protagonist finds these frozen ones. (who are later rrevived when they thaw out after being collected as specimines. They react with horror when they discover one of their number was dissected while frozen by the human scientists performing the expedition, go batshit on them, and murder the entire team except for the protagonist. They then retreat into the city, seeking the bunker.)
The ones that went below ground, of course, took the shoggoth with them, since they were by now completely dependent upon shoggoth labor. They had lost nearly all technological knowledge and were in a state of profound cultural and intellectual decay. The shoggoth turned on them shortly after the seal that closed off the city from the bunker below was erected, and massacred all of the elder things inside. Having basically been the actuall source of culture for some time now, the shoggoth assumed familiar patterns of construction, renovation, art installation, etc, and the bunker is their home. The Shoggoth's rapid expansion of cognitative ability stems from a sophisticated racial memory mechanism the elder things created them with. It radically reduced the time that shoggoth required from being a budding to being a functional laborer, as the new baby shoggoth was born with all of the memories and skills of all its parental lineage. Older shoggoth are less intelligent than younger generations, with linear growth of intellect over time. In short-- they are obscenely smart, and have a genetic hatred for elder things, which have enslaved and abused them for as long as they have existed. Another unfortunate side effect of this mechanism, is that... traits like sadism... are also propogated into the offspring. Meaning that each new generation can be more and more bloodthirsty, cruel, and sadistic. They take great pleasure in killing things.
Elder things are found all over the galaxy, so the failure of the earth colony site is inconsequential to them. Another fully functioning colony site of elder things that did not experience decay of this nature is breifly visited in Lights in The Witch House, Where the protagonist learns some hidden secrets about higher order geometry as it relates to spacetime (and thus, discovers a form of magic) purely through intellectual study, and unconciously travels to a triple star system with a planet inhabited by the entities. Thankfully he does not stay long, as the environment is not conducive to good human constitution, given that one of the stars is a blue giant and is clearly giving out intense UV light, as evidenced by his profound sunburn when he returns.
The position that Elder Things have toward earth based life, is that "We created it, we can do whatever the hell we want with it, it's our stuff." It should be noted that they do not have this view toward extradimensional entities, like the great old ones-- which they are afraid of, and venerate out of fear. Many intelligent lifeforms evolved from the period of their pinnacle to their late decline, including the "Polyps" (which they were eternally at war with) and the Yith (Another vegetable like animal form, that had a long neck stalk with tentacles on the end. They end up being the hosts of a body jumping spiritual parasite species from another planet, who displaces their intelligences wholesale, inhabiting their bodies, and leaving the displaced intelligences on their doomed world of previous occupation. By jumping to another living body before it dies, they can sustain themselves forever, and are the only "normal" race of beings in the universe to have conquered death. They are responsible for the creation of the Yithian Library.) As such, Elder Things are not too wowed by frail little things like Humans. (Or dwarves or elves.)