Each episode that they've appeared in has explained this.

  • The lone Dalek in Dalek was damaged and falling through time when the Doctor destroyed all of the Daleks and Time Lords, so it survived, and crashed on Earth in 1962.
  • The Emperor Dalek in "The Parting of the Ways" was in a time ship that was also damaged and falling through time, so the Emperor survived, ending up somewhere in space in the centuries between 190000-200000.
  • The other Daleks in "The Parting of the Ways" were created by the Emperor after the war.
  • The Cult of Skaro in "Doomsday" survived both the Time War and Rose's destruction of all Daleks by hiding in the void between realities in a special void ship.
  • The other Daleks seen in "Doomsday" survived by being inside the Genesis Ark, which was a prison ship built by the Time Lords to be cut off from the rest of space and time, and which was also inside the void with the Cult of Skaro.
  • Davros in "Journey's End" survived because Dalek Caan of the Cult of Skaro broke through the time lock and pulled him out of the War.
  • The Daleks in "Journey's End" were created by Davros from his own cells, after the War.
  • The Ironsides Daleks in "Victory of the Daleks" survived Donna's destruction of all of the Daleks by the same old crippled ship falling through time.
  • The New-Paradigm Daleks in "Victory of the Daleks" were created by the Progenitor device, which apparently wasn't destroyed in the war or any of the subsequent destructions of all Daleks because it wasn't in itself a Dalek.
  • All Daleks seen since then were created by the Progenitor device, the original New-Paradigm Daleks, and/or the empire they created in the future.