A temporal shift was a form of transport that was used to move beings through time and space to a new destination where the traveller would be safe. Emergency temporal shifts were normally used to make escapes, the traveller's power levels being greatly reduced from doing so, so as a result they could only be performed in times of great danger.
Whilst falling through the Time Vortex, the Dalek Prime Strategist of the Restoration Empire foresaw a much bigger war between the Daleks and the Time Lords. Not wanting to miss any of the action, the Strategist performed a temporal shift in an attempt to help the Emperor of the Restoration in the next battle the Daleks would face and, potentially, replace it to be the Emperor of the Time War. (PROSE: Exit Strategy)
According to the War Doctor, temporal shifts in the manner that the Daleks used them was an absolute last ditch option for escape. After losing a battle against Leela's force in the Obsidian Nebula, the last Dalek survivor attempted to escape via a temporal shift. It perished in the effort, instead opening a portal to the realm of the Unlived. (AUDIO: The Lady of Obsidian)
The Cult of Skaro escaped the Battle of Canary Wharf in 2007 through an emergency temporal shift (TV: Doomsday) and arrived in New York City in 1930. (TV: Daleks in Manhattan) Likewise, Dalek Caan used an emergency temporal shift to escape from New York after the Tenth Doctor foiled the plans of the Cult of Skaro and led the rebellion of the human-Daleks. With the other three Daleks dead, Caan alone escaped. (TV: Evolution of the Daleks)
Caan ended up in the Last Great Time War, which was time-locked. The time window to enter it was a mere fraction of a second, impossible to reach. Regardless, Caan entered at the cost of his own sanity and exposing him to the shifts of time so he could see many possible futures, but he was sane enough in the beginning while he used the chance to rescue Davros before his command ship fell into the jaws of the Nightmare Child. (TV: The Stolen Earth)
The Fifth Doctor performed a temporal shift to move the TARDIS away from an explosion. (AUDIO: Cobwebs) Cardinal Braxiatel stated that temporal shifts were relatively easy to engineer. (AUDIO: The Inquiry)