I have been reading The Lord of the Rings and it seems like men have basically no skills at all compared to elves and dwarves. Elves and dwarves are both excellent in craftsmanship, whereas the weapons/armor forged by men are barely heard of, barring the sword of Elessar. The average elf and dwarf are both much better at combat than an average man. I can understand that elves are good cause they have a 1000+ years to shape their skills but what about dwarves? Is it some sort of gift from Aulë?
As noted in another answer, Elves' skill can be explained, above all, by their very long lives in full adult vigor.
Dwarves are much closer to Men, but still have some inborn advantages. From the Silmarillion:
Since they were to come in the days of the power of Melkor, Aulë made the Dwarves strong to endure. Therefore they are stone-hard, stubborn, fast in friendship and in enmity, and they suffer toil and hanger and hurt of body more hardily than all other speaking peoples; and they live long, far beyond the span of Men, yet not for ever.
Both long-lived and from the beginning, made to be more hardy than any other speaking people. I don't think it was ever stated explicitly, but the people of Aulë (the craftsman among the Valar) all seem to have great skill in in making things. (IIRC, Sauron was in the beginning a Maia of Aulë.)
It isn't nearly as cut and dried as is frequently presented.
Aragorn is a king of Men and has the skill to prove it. Gandalf defers to his skill at healing and he matches wills with Sauron and wins (though it is a very close fight).
Frodo doesn't seem to have much power to speak of, yet all the Wise consider him to be a better ringbearer than they and he very nearly succeeds in destroying the ring on his own, faltering only at the final step.
The sword/dagger that destroyed the witch king was created by men as well and clearly the elves would have made wraith slaying blades if they had the ability. Powerful Numenorean artifacts are definitely rarer than their elven and dwarven counterparts, but some of that can be explained by Numenor's fall.
As others have pointed out, Men are the newcomers on the scene. Combined with their greatest accomplishments being drowned by the sea, it is easy to see why they don't have the sheer breadth of accomplishments that the other races have under their belt.
Men were able to make good weapons and armor and most of their warriors used weapons and armor made by Men and found it satisfactory. But the weapons and armor made by Elves and Dwarves was usually superior to that made by Men.
Only a few Men could afford to use Elf or Dwarf products (and Elves, unlike Dwarves, rarely sold their artifacts to Men).
Thus the great and famous leaders of Elves usually used swords and armor made by Elves or Dwarves, the great and famous leaders of Dwarves usually used swords and armor made by Dwarves, and the great and famous leaders of Men probably usually used swords and armor made by Elves or Dwarves because they could afford it, unlike ordinary warriors of Men.
So the great and famous leaders of Elves, Dwarves, and Men usually used weapons made by Elves or Dwarves, which sometimes became famous enough to be mentioned in LOTR, while ordinary warriors of Men used weapons and armor made by Men which rarely became famous enough to be mentioned specifically in LOTR.
The men of Numenor became more and more advanced in over three thousand years, and the men of Gondor retained some of that knowledge for a time after the Downfall. Thus many of their works, such as Orthanc, Minas Tirith, the Gates of Argonath, etc., seemed like wonders to the less skillful men of later in the Third Age.
And you might be interested in description of the Temple of Morgoth that Sauron had built in Numenor.
It seems to be as advanced as any domed structure built since Tolkien first described it.
WETA decided that Orthanc in the Lord of the Rings movies would be made of Obsidian, black Volcanic glass. There is a question asking if a tower like Orthanc could be made of Obsidian.
Answers say that obsidian would not be strong enough for such a large tower. My answer shows that Orthanc was impervious to attacks that easily destroys most stone. Therefore Orthanc must be made of an artificial material many times stronger than ordinary stone, but which looks like obsidian. A material unknown to modern materials science.
That means that the materials science of the Numenoreans at the time of the Downfall, and continued for a while by the Men of Gondor, was more advanced than that of our own era. The more medieval technology of men, even in Gondor, at the time of LOTR was the result of millennia of technological decline.
The outermost wall of Minas Tirith was made of the same or a similar material as Orthanc. The men of Gondor, with what remained of Numenorean science, were able to make vast amounts of artificial materials superior to those we can make. So no doubt the Men of Numenor also made superior alloys for some of their weapons and armor, but those weapons no doubt did not last for all 3,000 years until LOTR and so were not mentioned. They would have corroded or been lost over 3,000 years, and most of them would have been used in the Great Armament and lost with it.
Tolkien wrote many versions of his stories, and in some unpublished stories about Numenor the Numenoreans had steam and other engines for their ships, and perhaps even had aircraft.
It takes a lot to impress Elves. It takes even more to impress the holy Maiar. And it takes much, much more to impress the god-like Valar.
And when the Great armament of Ar Pharazon, the greatest force the world had ever seen - mightier than the (literally) millions (and possibly billions) of orcs of Morgoth, backed up by balrogs and dragons, and mightier than the army from Valinor that overthrew Morgoth - sailed for Valinor, the Elves and Maiar and Valar who had defeated Morgoth in (literally) world shattering battles all threw up their hands and exclaimed "God Almighty! Help us, oh God Almighty, because we can't fight such a powerful force."
Obviously the Elves, Maiar, and Valar in Valinor didn't think that the weapons and armor of Numenor were trash, since they literally called on Eru, God Almighty, to save them from the Great Armament!
Elves in LOTR are really different of what you might found in other genre like Dungeons and Dragons where there are smaller frail humans with longevity and better archery skills.
They are the first comers, they were meant to be superior beings. They are taller, stronger, near immortal, fairer and generaly a lot more poised than other beings. They are not necessarily smarter than men, but Elves can hone their skills for thousands of years, hence why they are great craftsmen, but if they are slayed, their knowledge is lost. That's what happened to Feanor and Celebrimbor who brought their talent in the grave.
Dwarves do have the gift of craft from Aulë, but they are generally oriented toward accumulating wealth. They make great big things in order to help them fulfill this ultimately unatteinable goal. That's why the rings of power didn't properly work. It only made them greedier and built to catastrophes like with Erebor or the mines of Moria. They also were there for a longer time and benefited from the teachings of the Elves earlier on.
That's the strength of men, their mortality. Tolkien likes to make weaknesses powerfull perks. Since men are mortal, they want to pass as much as possible to their heirs. That's why they build great things and answer the calls for fighting evil. Elves in a way paved the path for them to be the next in charge. Dwarves are meant to dig deeper and deeper until they lost all contacts with other creatures.