We don't have a definitive date for the construction of the North Stair, but given the scale of the project, it seems most likely to have been among the great works of the early Gondorians. The Stair may have been made later, for example at the time of the placing of the statues of the Argonath, which stood in the same general stretch of Anduin and were probably raised in approximately III 1250. Whatever the precise date of the Stair's making, it was explicitly said to be ancient by the end of the Third Age.

Actually Tolkien describes the Stair as the work of Númenóreans, so it possibly dated back into the Second Age, even before the founding of Gondor. However, in The Lord of the Rings, the Stair is explicitly connected to the Gondorians, so 'Númenóreans' here is a reference to the ancestry of the Dúnedain of Gondor, rather than the literal Men of Númenor.

From the account in The Lord of the Rings, it would be natural to assume that the North Stair ran down beside Rauros on the western side. It seems to have been part of Aragorn's original plan to use the Stair to descend into the lowlands, so the fact that he landed on the western shore, and that other Gondorian works were to be found there, would seem to imply that the North Stair was reached from the western side of the Falls.

To confuse matters slightly, however, Tolkien gives a definition for the North Stair in his extended index to The Lord of the Rings, and there he describes it as leading from the hills of Emyn Muil down into the Nindalf. Following the maps accompanying the book, the Nindalf lay on the eastern banks of Anduin, not the western. On the face of it, this seems rather odd - it hardly seems plausible that Aragorn meant to cross to the eastern bank, which was held by the enemy, to reach the bottom of the Falls. Alternatively, perhaps the Nindalf was rather wider than it appears on the canonical map, and included a region west of Rauros as well as spreading far to the east.