To be clear, I don't mean "by what means did the Ring physically change Gollum?", but rather "what were the overall physical changes affected on Gollum by his experiences after he found the Ring?". And by physical changes, I don't mean longevity or invisibility. I mean changes to his long-term physical form and appearance.
In the book The Two Towers, Gollum is effortlessly climbing head-first down a nearly sheer cliff face which Sam and Frodo only descended with great difficulty and the help of a rope. We read that he either had sticky pads on his fingers and toes (Tolkien compares them to those of an insect; I imagined a Gecko or tree frog), or else was able to use his "soft clinging hands and toes" to find and use "crevices and holds that no hobbit could ever have... used". It is strongly implied that Gollum does NOT, in fact, have sticky pads on his digits, but is using handholds and footholds that no hobbit could have used.
[As an out of universe side-note, I know many rock climbers, including free-climbers (i.e., rock climbers who don't use ropes); their hands are invariably covered in callouses and as hard as rocks themselves, so "softness" isn't particularly useful for climbing. In fact, as someone whose hands are huge, but delicate and soft as a baby's bottom, and who has only gone rock climbing a couple of times, I can assure you that soft hands are a serious disadvantage when rock climbing - your hands end up covered with more popped blisters and raw, bloody flesh than skin. Of course, Gollum isn't a rock climber, but he live in rocky caves for hundreds of years, so he should have callouses aplenty, not soft hands and toes. But I suppose this is neither here nor there.]
This was a bit perplexing to me because as we know, Gollum, however ghoulish he has become, is still technically a hobbit, as he has always been. So a hobbit was using handholds and footholds that no hobbit could ever have used.
This suggests that Gollum is anatomically very different from an ordinary hobbit in ways beyond his pallor, hairlessness, and large eyes. So I am wondering exactly what physical changes Gollum underwent after finding the Ring. Some may have been caused by his environment rather than the Ring itself. For instance, Gollum spent centuries in the dark; I assume this is why he became pale, and his eyes became larger than normal. He didn't eat much, or particularly well, which may have caused his extreme skinniness (especially relative to other hobbits). He never saw a dentist or brushed his teeth, so most of them fell out. He is centuries old and has a terrible diet, hence his baldness, perhaps.
But how else did he change physically after finding the Ring?