How the date is fixed
Vasant Panchami falls on the fifth day of the bright half of the lunar month Magha (Shukla Panchami). The date is the day on which that tithi is running at sunrise (the usual rule, called udaya tithi).
About
Vasant Panchami falls on the fifth tithi of the bright half of Magha, usually in late January or early February. The tithi prevailing at sunrise is taken, with the purvahna (forenoon) period preferred when Panchami spans two days. It is observed as Saraswati Puja in Bengal, Bihar and Odisha, where books and instruments are placed before the goddess. In North India it is the day children are traditionally introduced to writing, and yellow clothing and food recall the mustard fields in bloom.
How it is observed
Saraswati worship, the first lessons of children (vidyarambha) and wearing yellow are the usual observances.