Chinese New Year is the most-observed festival on earth and its date is determined by a rule that is astronomical rather than tabular, which distinguishes it from the Hebrew and ecclesiastical systems.
The calendar is lunisolar. Months begin on the day of the astronomical new moon, the true conjunction, calculated, not a mean value, and a month is 29 or 30 days accordingly. The solar year is divided into twenty-four jieqi, solar terms, each corresponding to 15 degrees of the sun's ecliptic longitude, alternating between twelve major terms and twelve minor ones.
The anchor is the winter solstice, which must fall in the eleventh month. That requirement drives everything else. If the interval between one eleventh month and the next contains thirteen new moons, a leap month must be inserted, and the rule for choosing it is that the first month in that interval which contains no major solar term becomes the leap month, repeating the number of the month before it.
New Year is then the new moon that begins the first month, which in practice is the second new moon after the winter solstice, occasionally the third. This places it between 21 January and 20 February.
Calculations are made for Chinese Standard Time, at 120 degrees east, which matters because a new moon occurring just before or just after local midnight shifts the date. Vietnam uses its own meridian, which is why the Vietnamese Tet occasionally falls a day apart from Chinese New Year, and once in a while a whole month apart when the leap months differ.