Dryads have occasionally appeared in works of fantasy fiction, most notably in C.S. Lewis' Narnia books, which maintains the distinction from hamadryads. In D&D, dryads and nymphs are different kinds of being, albeit with a number of similarities, but the latter did not make it into the 5E Monster Manual, something that's currently one of my criteria for including something in this series. In the first few editions they are, however, said to be "tree sprites"... but it's not clear what this means, since a sprite is yet another distinct creature in D&D, and one that resembles dryads rather less than nymphs do.
It also implies that they can only be found in forests with oak trees. The term "oak", however, can be interpreted quite broadly, and even includes some tropical species in places like Colombia and Indonesia. While oaks are not found in every country in the real world (especially in the southern hemisphere), even once we exclude those that don't have much in the way of forests, it's plausible to say that they're very widespread in a fantasy world.
Physically, dryads in 1E seem to resemble elven women and dress in a similar style. Their two hit dice - more than a starting character or, say, a typical orc - implies a fair degree of physical resilience, but they clearly aren't fighters. We're told that they're typically armed only with daggers, which they use only as a last resort in self-defence, and they're one of the few creatures to have the lowest possible armour rating. The text implies they are solitary, but, in fact, they seem to live in groves with up to six members.
They are slightly more intelligent than typical humans and, as so often, have their own native language not shared with other beings. Unusually, even for fey, they don't typically speak Common, although they do speak Elven and a couple of more obscure languages. They can also communicate with plants, which is likely linked to their stated innate sense for what is happening in their forest (I'd interpret this as something like communing with the Green in the Swamp Thing comics, but it's unlikely to be the way Gygax envisaged it). Like satyrs, they are inherently resistant to magic.
The illustration shows that dryads carve a home out of their tree, living in it in an at least approximately human-like manner. The text, however, contradicts this, implying that it's not possible to categorically identify a dryad's tree even with the aid of magic. This, no doubt, is to help them escape from hostile PCs, since combat clearly isn't their purpose in the game.
2EIn most respects, the 2E dryad is the same as her 1E counterpart. The description, however, is more detailed, adding the fact that their hair and skin colour change with the seasons; the former turns green in spring and summer, but they are otherwise visibly indistinguishable from elves.
There's also further information on the dryad's bond with her tree, stating that she takes damage as it does, and dies (usually within 24 hours) if forcibly carried away from it. Dryad groves, implied to be the normal mode of life in 1E, are now stated to be a rarity, and it's clarified that the individual members of the grove barely interact with one another unless they have to. So, very antisocial, then.
They are better at combat in other respects, too. They now have four hit dice (better than gnolls), and, while their skills are primarily focussed on non-combat traits such as perception, stealth, and knowledge of nature, they can use longbows as well as daggers. They have access to a wider range of magic than before, all of which is, of course, nature-oriented. They can also travel nearly three times further from their tree without ill effect than they could before.
On the subject of which, it no longer has to be an oak tree, making such things as pine and eucalyptus dryads a possibility.
Culturally, while groves are rare, as they were in 2E, they are slightly larger when they do occur. Previously described as "Neutral", which makes sense for being so shy and avoidant of others, they are now Chaotic Good, active defenders of the forests in which they live and showing more compassion to those who do not directly threaten them. They now share a language with other fey beings, and regularly speak Common as well as Elven.
In combat, they now use clubs instead of knives - largely because there's a druid spell that makes that advantageous, and which they have access to. The longbows have gone, but they're still reasonably effective in a fight. They're also far more sociable, at least with other fey (they've switched back to being Neutral), and regularly cooperate with unicorns, satyrs, and the like. They can also communicate with wild animals as well as communing with vegetation, but have lost the ability to speak Common again.
The bond with their tree has weakened further since 3E. Although they don't like to travel too many miles from home, it's clear that there is no hard and fast limit to this and they can move through the forest more or less as they will. They don't take damage when their tree does (this doesn't seem to be the case in 3E either) and, even if it's destroyed they go mad rather than actually dying. Presumably, they do die if the tree dies a natural death, but this isn't explicitly stated, and, in any case, could take hundreds of years.
Dryads are, like many other races derived from Greek myth, portrayed as having only one apparent gender. In the original myths all dryads were female, and this is almost universal in both D&D and other fantasy RPGs that include the race. (Pathfinder is an unusual exception). However, they don't seem to be parthenogenetic, but rather created magically, either as a spontaneous effect that sometimes occurs in older trees or as a deliberate creation by powerful fey beings.
This makes it easier to see how they end up avoiding other humanoids, having had no parents or social upbringing, although it does imply that they shouldn't have anything but the simplest of tools, and certainly no iron daggers. Dryads do, however, become steadily less antisocial as the editions progress, moving from extremely shy and retiring beings to stalwart defenders of natural woodlands. In parallel with this, they become more effective in a fight and gain a wider range of magical abilities.
However, there are two core abilities that remain with dryads throughout all the versions. One is an ability to magically step into a nearby tree and emerge from a different one elsewhere. The details change between editions, but it seems mainly intended as an escape route. This, however, is not what I'd describe as their signature power, because that is their ability to Charm.
And that changes rather more dramatically.
In both 1 and 2E, dryads can use magic to charm a person into helping them. If someone is charmed they are "taken away" and will not return for several years, if at all. Quite how they are "taken away" is unclear, since the dryad still has to remain within 120 yards of her tree. Perhaps the intent is that the dryad can grant her thralls the ability to merge into trees as she does, making it all but impossible for anyone else to rescue them without laying waste to the surrounding forest, chopping everything down within sight.
1E also doesn't say what the victims are taken away for, although the fact that dryads tend to do this with physically attractive men rather gives one a hint. 2E however, is unambiguous; the thrall becomes a willing sex slave.
And this, it would seem, is the real point of dryads in the first two editions. They are there to enslave men, to be an obstacle rather than a physical threat. The fact that dryads are physically attractive adds a layer of masculine wish-fulfilment to this, perhaps something that's meant to be taken as a bit of a joke, even if it's effectively the end of a charmed PC.
3E, perhaps less willing to be seen as encouraging potentially juvenile jokes, not only removes this motivation but specifically states that it's a myth, and nothing of the sort ever really happens. Here, charmed individuals are typically sent out to further the dryad's mission of protecting the forest... and the effect lasts for six hours, not for several years. In 5E it lasts for 24 hours, but can only be used on one person at a time. Interestingly, though, it does hint that dryads sometimes use the ability on particularly attractive individuals, implying a sexual motivation, even it's now only for a brief fling.
One might also note that for the first time 5E, and this is probably deliberate, uses gender-neutral language to describe the objects of a dryad's affections...
While a number of other systems already have dryads, or something very similar, duplicating the D&D version in them depends a lot on the edition being emulated. There is a general agreement that dryads are more intelligent than humans, but, in most cases, they are physically similar to an average, non-combatant human. In 3E and 5E they have reasonable, if not especially broad, combat skills, although these may be heavily reliant on nature magic to back them up. In 1E and 2E, they have virtually nothing, with their skills entirely focussed on perception, stealth, and woodland crafts.
They do, however, have a very high charisma, usually around the human maximum. Depending on the version, this might represent an advantage such as Attractive, but it's more likely to describe a persuasive personality, with the dryad being able to charm people with her words as well as her magic. In some systems, that's likely to be a skill rather than an attribute, but if the system allows for both, it's probably just an attribute/trait - raw talent rather than social expertise, given their lifestyles. As for the magical Charm powers, the shorter-term version is surely more gameable, and can probably be based on an existing spell.