How the date is fixed
Ganga Dussehra falls on the tenth day of the bright half of the lunar month Jyeshtha (Shukla Dashami). The date is the day on which that tithi is running at sunrise (the usual rule, called udaya tithi). In a year with an adhika (extra) Jyeshtha, it is kept in the adhika month†.
About
Ganga Dussehra falls on the tenth tithi of the bright half of Jyeshtha, in May or June, and recalls the descent of the Ganga from heaven to earth. Its name, Dashahara, is read as 'that which takes away ten', and the texts list ten conditions that can meet on the day, among them the month of Jyeshtha, Shukla Dashami, Hasta nakshatra and a Wednesday; almanacs choose between two days by how many of them meet. This site takes the Dashami at sunrise. In a year with an adhika (extra) Jyeshtha it is kept in the adhika month, as the almanacs print it.
How it is observed
Bathing in the Ganga or another river, lamps floated on the water at dusk, and the Ganga aarti at Haridwar and Varanasi.