The oldest source I am aware of that mentions the forging of Arthur's sword is Geoffrey of Monmouth's Historia Regum Britanniae, a Latin pseudo-history of the British isles composed around 1136. A complete Modern English translation may be found here, which is the source of the quotes below.
Also Arthur himself, having put on a coat of mail suitable to the grandeur of so powerful a king, placed a golden helmet upon his head, on which was engraved the figure of a dragon; and on his shoulders his shield called Priwen; upon which the picture of the blessed Mary, mother of God, was painted, in order to put him frequently in mind of her. Then girding on his Caliburn, which was an excellent sword made in the isle of Avallon, he graced his right hand with his lance, named Ron, which was hard, broad, and fit for slaughter.
Here, Arthur's sword is identified as "Caliburnus" in the original Latin. Although that name was sometimes assigned to the Sword in the Stone (when the two weapons are taken to be different), the Historia predates the earliest known reference to the Sword in the Stone tale, which is not known to have appeared until around the end of the twelfth century. Moreover, the name Caliburnus is a Latinization of the Old Welsh Caledfwlch (or perhaps the later Cornish cognate Calesvol or a similar cognate from another insular Celtic language), the oldest attested name for Arthur's magic sword. The subsequent development in Old and Middle French to Excalibur is well documented, including the clearly intermediate form Caliburc from the Estoire des Engleis, which probably dates to slightly after Monmouth's Historia. (Wikipedia has a reasonable summary of the development of the name.)
So According to Geoffrey, the sword was forged on the mystical isle of Avalon, but no further details are provided, and the sword itself is not a major part of the story—except insofar as it was Arthur's primary weapon.
... neither did he give over the fury of his assault until he had, with his Caliburn alone, killed four hundred and seventy men.