The Sub-Wave Network was a piece of sentient software programmed to find anyone who could help to contact the Tenth Doctor. It used sub-wave communication to transmit, which meant it was undetectable as it was below normal waves. It was created by the Mr Copper Foundation and further developed by Great Britain's former Prime Minister Harriet Jones.
The network found Captain Jack Harkness at the Torchwood Hub, Sarah Jane Smith and Luke at 13 Bannerman Road, and Martha Jones at her house with her mother in London. It also found Rose Tyler at Donna Noble's house but she was unable to communicate with anyone since the laptop she was using did not have a webcam.
As Martha Jones' superphone temporarily did not function, Torchwood and Sarah Jane used the power of the Rift, Mr Smith, and every single telephone on the planet to call the Doctor with the number from the superphone, managing to get through the Doctor's TARDIS so that he could find where the Daleks had taken Earth.