Each side was lead by battle-computers to calculate the enemy's moves. However, each computer could predict the other's moves so well that they were locked in a stalemate. Hundreds of Dalek battlecrusiers and Movellan battlecruisers flew with each other for hundreds of years without firing one shot as a result of this.
In an attempt to win the war, the Daleks returned to their homeworld of Skaro to seek their creator Davros while the Movellans traveled to Skaro to destroy the planet at Davros with the Nova Device. Hoping Davros would reprogram their battle-computers, the Daleks revived him and a small battle was fought on the planet with the Doctor interfering in the battle, deactivating the Movellans, destroying the Daleks, and placing Davros in a cryogenic freezer.(Destiny of the Daleks)
The war continued with the Movellans developing a virus that attacked and destroyed Daleks. It is unknown how the war ended but it eventually lead to a civil war between the Daleks.(Resurrection of the Daleks)
Later on, after the civil war, a later incarnation of the Doctor was told by the Dalek Prime that the Movellans were created by the Daleks and that the whole war was a play to protect Skaro from destruction. This is not understood as this information would contradict with other history.(War of the Daleks)