Chronologically, from the Galactic point of view, the war began in the late 54th century, soon after the Second Galactic War. However, battles in the war took place across all of time and even in the Time Vortex itself. The War basically annihilated both races, with only a few members of each race surviving on both sides. The Doctor and The Master were the only two Time Lords (who were biologically still Time Lords) to survive, and the Cult of Skaro were the only Daleks to survive, until they began rebuilding the Dalek Empire.
Dalek Caan attempted to break through the Timelock of the War to rescue the Dalek's creator, Davros. However, his Passage of Time was shattered by Dialga whom Caan came face-to-face with. After acknowledging the existence of a being superior to the Daleks, Caan was driven insane and Dialga, sensing a way to stop the Dalek's meddling with Time forever, showed Caan all of Time, which convinced him that the Daleks had commited atrocities that put them beyond redemption. He allowed Caan into the War, in order to execute his plan, which consisted of wiping out the Imperial Daleks using Davros as the catalyst.Time Travel meant that the Daleks were actually losing.
However, the Daleks were capable of many more atrocious acts. They razed cities, killed millions and destroyed planets just to wipe out the Time Lords. Eventually the war reached the Time Lord's homeworld of Gallifrey.
The brutal tactics of the Daleks slaughtered millions, Men, Women, Soldiers and Children were all slain in the conflict. The Dalek Fleet above Gallifrey razed the Time Lord city of Arcadia, and the Doctor himself fought to protect the city. As the Daleks advanced on the Time Lord Citadel, the Doctor realised he had to take action. In a desperate move, the Doctor was forced to activate the Time Lord relic called the Moment, which supposedly destroyed everything in the Time War and slaughtered millions of Daleks and Time Lords. This act weighted heavily on the Doctor's conscience, and fuelled his desire to save as many races from danger as possible.
However, it was later revealed that the Doctor had not killed all the Time Lords, and that the entire planet of Gallifrey was saved from the War. After encountering the Tenth and Eleventh Doctors who had travelled back to stop the War from ending in such a brutal way, the Three Doctors came up with a new planet to transport Gallifrey into a pocket universe. The Dalek Fleets in orbit above the planet were firing upon Gallifrey constantly, and when the planet magically vanished the entire Dalek Fleet was wiped out in their own crossfire. The Time War was at last over, and this time, there was a clear victor.