How the date is fixed
Vijayadashami falls on the tenth day of the bright half of the lunar month Ashwina (Shukla Dashami). The date is the day on which that tithi is running at aparahna, the afternoon.
About
Vijayadashami is the tenth tithi of the bright half of Ashwina, in September or October, the day after Navratri ends. The governing period is aparahna (afternoon): the day whose afternoon carries Dashami is chosen, and Shravana nakshatra in that window is considered especially fitting. It is one of the sade-teen muhurta days of the muhurta tradition. North India burns effigies of Ravana at dusk, Mysore holds its royal procession, Bengal immerses the Durga images, and in Maharashtra and the Deccan leaves of the Shami tree are exchanged as 'gold'.
How it is observed
Shami puja and crossing the boundary (simollanghana) in the afternoon, Ramlila and Ravana dahan at dusk, and Durga immersion in the east.