Narsil, the sword of Elendil, is not - despite all appearances - an elvish sword. Nor was it made in Numenor. In fact, it was forged by Telchar, a Dwarf of Nogrod (and thus presumably either a Firebeard or a Broadbeam, with a possible preference on the former). Telchar also forged Angrist, the knife of Curufin which Beren used to cut through Morgoth's iron crown. He also made the Dragon-helm of Dor-lomin, which apparently struck fear into the hearts of its wearers enemies.
Angrist was made for Curufin, son of Feanor, and it's tempting to think that Narsil was the same. But should we? Narsil lacks the supernatural sharpness of Angrist - we see Aragorn wearing Narsil sheathed, while Angrist had to be kept uncovered because it would cut through any scabbard. It hardly seems likely that Curufin would take a dwarven sword over an Elven one - he was a smith himself, his father was accounted the greatest of all Elven smiths, so I really can't see him admitting that a dwarf could do better general purpose work, rather than the specific art of ultra-sharp weapons. Could it, instead, have accompanied the Dragon-helm?
Well... no. The helm was actually made for the Lord of Belegost, a dwarf. It was given by him as a gift to Maedhros, and thus passed to Fingon, Hador of Dor-lomin, Galdor, Hurin, and finally Turin. The idea that a sword would have followed its path exactly is unlikely to say the least.
So how did Narsil reach Numenor, and specifically Elros, first King of Numenor? The options are limited. It may have been given to him by Maglor, his foster-father, thus keeping the connection to the Sons of Feanor in place; since Curufin was the only Feanorion known to spend time with the dwarves, this would bring us back to him accepting an 'inferior' blade. Or, more interestingly, it could have been given by the dwarves to someone else.
My discussion of Lady Haleth of Brethil reveals that she was a friend of the dwarves of Nogrod and Belegost - could Narsil have been their gift to her, and to her successors? Could it even be the sword that Brandir, last Lord of Brethil, bore when he went to confront Turin? Certainly that sword was significant in some way - the Haladin usually fought with axes, not swords. The Haladin formed a small part of the founders of Numenor - they could easily have passed their emblem of leadership to their new king as a sign of loyalty.
Connecting Brandir's 'short sword' with the long, two-handed Narsil/Anduril we know may seem difficult - except that in the books, Aragorn wields it with a shield at the Hornburg, while Boromir's similar blade is always used in conjunction with a shield. While Narsil is very impressive as a long blade, the evidence suggests it is rather shorter than we think.
So, having reached Elros, how did Narsil end up held by Elendil, who was not in the direct royal line? One could well ask the same question about the Ring of Barahir, the other emblem of leadership of a nearly-destroyed House of the Edain. That ring was given by Tar-Elendil to his daughter - who would have been his successor had the laws of inheritence allowed it - and by her to Valandil, first Lord of Andunie, and ancestor of Elendil. Tar-Elendil was the king who first sent expeditions back to Middle-earth; could it be that his possession of the heirlooms of the 'old Houses' fed speculation that he was more interested in the old world than in Numenor? His passing of both the Ring and the Sword to the ancillary line of Andunie could have been a political gesture, not simply one of kindness.