The Cybermen were the first to appear, as they disguised themselves as Ghosts. The Torchwood Institute helped them get through with a large object known as the Sphere. Then when the time was right some of the Cybermen activated and sent their assistants to open up the Sphere. The Sphere, a ship designed to navigate the Void between dimensions, had no weight, no mass and no heat. Then the Cyber Workers were killed and the Cyber Leader arrived and killed 2 Torchwood Ghost Shift Scientists. Then the Sphere opened up and the Ghost Shift was increased to 100%. Every single Ghost was a Cyberman and there were millions across the world. In the Sphere Chamber Rose, Mickey and Dr Rajesh Singh saw what came through. Mickey thought it could have been a Cyberking or a Cyber Emperor
Then the Daleks were known as the Cult of Skaro and had names Dalek Sec, Caan, Thay and Jast. They had a Genesis Ark with them which held millions of Daleks and was Time Lord Technology. Dalek Thay went to investigate and met 2 Cybermen. Then the Cybermen spoke to Thay and then he spoke back. They wanted to identify each other. Then
The Daleks declined the Cybermen's offer of ruling Earth together. But when the Cybermen fired the Cult of Skaro had force fields as then Thay exterminated the Cybermen. Dalek Sec and the Cyber Leader declared War against each other 5 million Cybermen Vs 4 Daleks. Then later on in the Sphere room Jake, some of his Troops and some Cybermen fought against the Daleks but failed to wound them. At this point the Cybermen began upgrading the Torchwood Staff like Yvonne Hartman. The Daleks then proceeded to Torchwood's Alien artifacts room and fought against the Cybermen and the remaining Torchwood Staff.
Then the rest of the Cybermen headed back to the Torchwood Tower to help the Cybermen there. Dalek Sec filed up with the Genesis Ark and released the trapped Daleks. Then 5 Cybermen including a Cyber Leader were heading up to the main part of Torchwood until Cyber Yvonne Hartman remembered herself and killed the Cyber Leader and his Troops. The Daleks in the skies fought against the Cybermen on the ground. The Doctor and Rose held onto 2 Clamps and released the Voids doors. The Daleks and Cybermen flew inside it but one of the Controls blew. Rose let go of her Clamp and pushed it up, by this point the remaining Cybermen and Daleks flew into the Void. Dalek Sec and the Cult of Skaro Emergency Temporal Shifted. The Doctor saved Earth but lost Rose Tyler. There was a list of the Dead of the Battle at Canary Wharf with hundreds of people's names on it.
They appeared in Series 2: Army of Ghosts and Doomsday
Here is a video of the Battle of Torchwood between these 2 monsters: