Once it is day, it becomes night after a turn in which the active player cast no spells, and day again after a turn in which they cast two or more.
The rule
Day and night belong to the whole game, not to a player. A game starts as neither (CR 731.1). Cards with daybound and nightbound make it day or night; from then on it switches by itself.
When it is day, it becomes night if the player whose turn it was last turn cast no spells during that turn. When it is night, it becomes day if that player cast two or more spells during that turn (CR 731.2a, CR 731.2b).
With shared team turns, as in Two-Headed Giant, the spells of the whole team count (CR 805).
In Life Counter
Day and night is one token for the whole table. It reads Day/Night until a card sets it, then shows day or night, and a tap switches it.