The war started when the Doctor implanted some Daleks with 'the human factor' and caused them to revolt. Afterwards, the Supreme Dalek starting fighting against Davros, the creator of the Daleks, and he joined the Imperials. The ideological differences between the factions mean that they see each other as two different species, when in fact there is little difference between the two.
There were many tactics employed by both sides to win the war, and one of these tactics was the Imperial Special Weapons Dalek, an 'Abomination' that uses dangerous heavy weapons to annihilate Renegade Daleks on the spot.The two factions of Daleks fought each other for many years, devastating their homeworld of Skaro and any other worlds they fought over. Any races caught in the crossfire were destroyed completely. There was Galactic outcry, but no-one wanted to interfere with the war for fear of being destroyed. Even the League Military opted to remain neutral, because there was no way they could decide who to side with. And even if they did side with one, the losses they would face fighting against the other seemed pointless for a conflict that was too similar to petty in-fighting (which the League Military remains strictly neautral in). Not only that, the League was concentrating on the Rachni Wars at this time. The war stretched on and on, getting worse and worse with every conflict. As planet after planet fell, Galactic citizens began to wonder if there was any end to the carnage. Some thought it was a a massive Dalek scheme, an excuse to destroy everything in existence. Eventually the war reached the Human homeworld of Earth. Both factions came to Earth looking for the Hand of Omega, a Time Lord weapon designed to engineer stars. Neither side managed to get it however, as the Doctor reached it first. He reprogrammed the Hand to turn against the Daleks, and it destroyed them all and burnt their homeworld to a cinder. The remains of the Dalek Empire regrouped and turned their attention towards the Time Lords, and began the Time War.
To this day, no-one kmows who won the war, or if it has even over. But for the citizens of the Galaxy, the worst is definatly over.