The ghem-lords of Cetaganda were seeking expansion of their empire, and weren't above the use of thoroughly nasty means of bringing it about. The prison camps on Dagoola were particularly egregious examples of mistreatment of tens of thousands of prisoners (there were at least three camps, probably more, since Dagoola IV Top Security Prison Camp 3 was filled to capacity).
The war appears to have begun some time during '95 Earth Common Era, when Miles Vorkosigan was 22 or at most 23. It had not started at the time of the death of the old Cetagandan empress Lisbet Degtiar, during which time Miles Vorkosigan was 22, though Ambassador Vorob'yev of Barrayar was predicting the coming of such a war at that point.
The war ended when Miles Vorkosigan was 28; thus, it was about six years in duration.