The New Dalek Empire was founded by Davros in the aftermath of the Last Great Time War, which destroyed the original Dalek Empire. Davros apparently lost some control of the Empire, which fell under the reign of the Supreme One.
Overview
The New Dalek Empire was very different compared to the Dalek forces that appeared after their empire's supposed destruction in the Time War. (DW: The Parting of the Ways) They were not survivors using scattered technology but rather a true empire and quite capable of combating Time Lord technology. They were even capable of capturing and disabling a TARDIS. Their forces consisted of hundreds of starships with enough power to devastate the universe. Their central base of operations was the Crucible where they planned to reside on when the reality bomb destroyed the universe. (DW: Journey's End)
First Attempts
The New Dalek Empire was to be the new Empire of the Daleks that the Cult of Skaro had planned to create. The very first attempt was on planet Earth with the Genesis Ark, to unlock it and unleash the Daleks within, of which the Doctor thwarted. (DW: Doomsday) Time travelling from London in 2007 to New York City in 1930, the Cult, now the last four Daleks in existence, attempted to conquer Earth and recreate the Dalek Empire.
This attempt, even with the help of the Final Experiment (which included use of Pig slaves and human-Dalek hybrids) failed due to the interference of the Tenth Doctor. At the end, Dalek Caan was the last surviving Dalek in all of creation. (DW: Daleks in Manhattan / Evolution of the Daleks)
New Empire
Caan activated an emergency temporal shift to escape the Doctor, and ended up at the Gates of Elysium during the Last Great Time War. Travelling into a time-locked era ruined his mind, but he helped to save Davros from his death. Davros, like the Dalek Emperor who also survived the Time War by time travel, rebuilt the Dalek Fleet of two thousand ships and millions of Daleks - unlike the Emperor, Davros rebuilt the Daleks out of his own Kaled cells. Caan was left as a sort of prophet, and a new Supreme Dalek was created to oversee the Dalek forces.
In 2009, the Daleks moved 27 planets into the Medusa Cascade from various times and places (mostly the present, but from other eras as well). The new Daleks then took control over the planets in the Cascade. In their attack on Earth, they took many humans aboard their ships, and wiped out any resistance that they met. (DW: The Stolen Earth)
The new Empire planned to use the 27 planets in the Medusa Cascade in conjunction with the Crucible's energy source to power a Reality bomb created by Davros. This would have led to the destruction of all of existence and allow the Daleks to be the sole inhabitants of the universe. However, through Dalek Caan's manipulation of the timeline, Donna Noble shut down this device. The Meta-Crisis Tenth Doctor finished off the fleet by overloading and feeding back the Dalekanium. (DW: Journey's End)
The Empire was destroyed, but several Daleks survived this attack. (DW: Victory of the Daleks, SP: The Doctor Who Experience)