'Stair' is PIE *steygh- (to stride, to climb) — the same root as 'stile' (steps over a fence).
Each of a set of fixed steps leading from one level to another; also used in plural ('stairs') for the whole set.
From Old English 'stǣger' (a stair, a flight of steps), from Proto-Germanic *staigriz, from the PIE root *steygʰ- meaning 'to stride, to step, to climb.' The same root produced Greek 'steikhein' (to march in order), Old Irish 'tíagaid' (they go), and, through a different Germanic derivation, the English word 'stile' (steps over a fence). The original concept was the act of climbing
English 'stair' and 'stile' (steps over a fence) are from the same Proto-Germanic root *staig- (to climb). A stile is etymologically a 'climb-over' — the same climbing concept applied to a fence rather than a building, preserved in the nursery rhyme 'There was a crooked man who walked a crooked stile.'