Where did the Noldor learn to fight?

Question

Melkor had no reason to suspect that Fëanor or his kin would have any ability as warriors:

It may be that he feared him little, for he had as yet no proof of the swords of the Noldor

And yet, fighting against the forces of Melkor, bred for war,

The Noldor, outnumbered and taken at unawares, were yet swiftly victorious

So we can infer that the Noldor were skilled warriors. Are there any canonical references to the Noldor (or Elves in general) having an innate fighting ability, or of their training for war?

Answer 1

Tolkien’s battles were not won merely by strength or skill in fighting.

A key thing to note before discussing where the Noldor may have learnt to fight is discussing what it meant to be powerful in Tolkien’s Legendarium.

Tolkien didn’t have a conventional sense of power, the strongest fighter amongst the Valmar, Tulkas, was nowhere near the most powerful. Tolkien was a Christian and had a deep interest in Norse Mythology. Power was granted by God unto his creations. The Elves were imbued with great strength and will. The Elves also had other, more mystic power. They existed in both the physical world and in the spiritual world, and around them there was a glow. The Elves were granted greater power and beauty unto them, and were the closest to the Ainur of the Children of Ilúvatar. As such they would, according to the will of God and fate, be more powerful than Orcs.

The dealings of the Ainur have indeed been mostly with the Elves, for Ilúvatar made them more like in nature to the Ainur, though less in might and stature...
_{The Silmarillion, Quenta Silmarillion, Chapter 1 - Of the Beginning of Days}

They passed slowly, and the hobbits could see the starlight glimmering on their hair and in their eyes. They bore no lights, yet as they walked a shimmer, like the light of the moon above the rim of the hills before it rises, seemed to fall about their feet.
_{The Fellowship of the Ring, Book One, III - Three is Company}

Then the Witch-king laughed, and none that heard it ever forgot the horror of that cry. But Glorfindel rode up then on his white horse, and in the midst of his laughter the Witch-king turned to flight and passed into the shadows.
_{Return of the King}

A great example of the power in a person is Fëanor, who was considered the greatest of all Elves in skill and strength amongst other things. His voice so powerful he forced the herald of the Valar to bow before him.

In that hour the voice of Feanor grew so great and so potent that even the herald of the Valar bowed before him as one full-answered, and departed...
_{The Silmarillion - Of the Flight of the Noldor}

The might of the Elves has also waned since the days of Old. Greatest were they shortly after awakening and their departure from Cuiviénen.

In the beginning the Elder Children of Ilúvatar were stronger and greater than they have since become...
_{The Silmarillion, Quenta Silmarillion, Chapter 3 - Of the Coming of the Elves and the Captivity of Melkor}

The Noldor were great amongst the Eldar, quick to learn, and more skilful than the other houses:

Noldor] meant 'the Wise', that is those who have great knowledge and understanding. The Noldor indeed early showed the greatest talents of all the Elves both for intellectual pursuits and technical skills.
_{History of Middle-earth XI The War of the Jewels "Part 4. Quendi and Eldar" Part C: The Clan-names "Noldor"}

It is likely that given their prowess they had learnt quickly from the teachings of the Valar after their arrival in Valinor and quickest amongst the Elves learnt to hunt and fight.

Tolkien, however, never explicitly states how they learnt to fight

At Cuiviénen, the Elves had lived hidden for a while. At some point they were found by Melkor, and him they feared, as Elves wandering alone or in small groups would disappear and not be heard from again.

... So it came to pass, some years ere the coming of Oromë, that if any of the Elves strayed far abroad, alone or few together, they would often vanish, and never return...
_{The Silmarillion, Quenta Silmarillion, Chapter 3 - Of the Coming of the Elves and the Captivity of Melkor}

It is possible that to hunt and to defend themselves against the spies of Melkor, the Elves had learnt some primitive form of fighting, or at least defence.

Later, Oromë, the Hunter, found the Elves, and after looking on for a while he made himself known to them, and lived with them for a while. While Oromë wasn’t Tulkas, he was an expert Hunter and would likely have taught the Elves much during his time with them, if not he would certainly have taught them at least one thing, to hunt.

Oromë tarried a while among the Quendi, and then swiftly he rode back over land and sea and brought tidings back to Valmar...
_ibid.

Answer 2

Not explicitly mentioned, but presumably in Valinor

The Noldor were said to be "great in knowledge and of skill". While not explicitly saying that they were good at fighting, it does tell us of their resourcefulness and thirst for knowledge.

In Valinor the Elves were taught many things by the Valar, and notably so for the Noldor was the art of craftswork by Aule.

Feanor and his sons abode seldom in one place for long, but travelled far and wide upon the confines of Valinor, going even to the borders of the Dark and the cold shores of the Outer Sea, seeking the unknown. Often they were guests in the halls of Aule; but Celegorm went rather to the house of Orome, and there he got great knowledge of birds and beasts, and all their tongues he knew.

It may not be too farfetched to say that other Valar, Tulkas for example, taught the Eldar, including the Noldor, how to fight and defend themselves. Clearly the Valar knew how to and demonstrated it in The First War with Melkor, so it would seem natural for them to impart some useful combat skills to the Eldar.

Their eagerness and innate skill in learning new things, together with their immortality, are probably the reasons why the Noldor were so adept at fighting.

Aule it is who is named the Friend of the Noldor, for of him they learned much in after days, and they are the most skilled of the Elves; and in their own fashion, according to the gifts which Iluvatar gave to them, they added much to his teaching, delighting to tongues and in scripts, and in the figures of broidery, of drawing, and of carving.

---

The Silmarillion also says this:

Next came the Noldor, a name of wisdom, the people of Finwe. They are the Deep Elves, the friends of Aule; and they are renowned in song, for they fought and laboured long and grievously in the northern lands of old.

Which tells us, as the question also states, that by the time the Noldor reach Middle-earth they knew how to fight (and notably quite well). That leaves us with the assumption that they learnt how to fight in Valinor, as there was no place else they visited after leaving Middle-earth for the first time.