How the date is fixed
Ganesh Chaturthi falls on the fourth day of the bright half of the lunar month Bhadrapada (Shukla Chaturthi). The date is the day on which that tithi is running at aparahna, the afternoon.
About
Ganesh Chaturthi falls on the fourth tithi of the bright half of Bhadrapada, in August or September. Ganesha's birth is placed at midday, so the madhyahna period governs: the day whose midday holds Chaturthi is chosen, and the installation and puja are done in that window. The ten-day festival that follows ends with immersion on Anant Chaturdashi. Tradition advises against looking at the Moon on this night, which is the origin of the Syamantaka story read as an antidote.
How it is observed
A clay Ganesha is installed at midday, worshipped with modak and durva grass, and immersed after one and a half, five, seven or ten days.