In the ShowEdit
In the first five seasons of Doctor Who, the Time Lords neither appear nor are mentioned by the Doctor. However, in the Season Six finale, The War Games, the Doctor finally reveals his race to companions Jamie McCrimmon and Zoe Heriot. During the episode, he finds himself facing against the war-loving race the War Lords, as they kidnap various historical figures from time and space and force them to fight in various battles. To stop them, the Doctor summons his people to the planet, only to be caught by them while trying to escape.
After being put on trial, the Doctor manages to convince his people to spare him the death penalty for his crimes (stealing an Type 40 TARDIS, interfering with history and 'kidnapping' other beings). Agreeing, the Time Lord exile the Doctor to Earth, where he remains there until they release him from the exile for stopping Omega in 1972/3's The Three Doctors.
The Three Doctor also explains how the Gallifreyans, the original name for the Time Lords, discovered time travel. In it, the Doctor states that he was taught that Rassilon, founder of the Time Lord society, and Omega, the villain of the serial, neutralized a star between the point of becoming unstable and becoming a black hole, which they then used to access the Time Vortex. Omega, during these events, became trapped in the Anti-Matter Universe. It is hinted during the episode that Rassilon might have done this on purpose. If so, he would have been self-loathing, like many to follow.
During 1976's The Deadly Assassin, the Doctor is summoned back to Gallifrey, only to be framed by the Master for assassinating the President of the Time Lords. During which, the Doctor uncovers a conspiracy involving Goth, a politician who desired to become the next President, and the Master. Goth is killed during the events of the serial, only to have the truth covered up by others to keep his legacy intact.
Over the next years of his travels, the Doctor would also discover various schemes by individual Time Lords who tried to gain power. One of these included him being placed on trial by a 'future' incarnation called the Valeyard. The Doctor also travelled with Time Lady Romanadvoratrelundar, or as he called her for short, Romana.
During the Revived series, it was believed that the Doctor destroyed the Time Lords along with Gallifrey and the Daleks. In the 2009 Christmas and 2010 New Year's Day specials, the Doctor reveals to Wilfred Mott that he did so because the President at the time, a resurrected Rassilon, planned to escape the time-lock set upon the war and destroy both time and space. The Time Lords would of course live on as sentient beings, similar to one of the Doctor's foes, the Great Intelligence.
The Doctor, at the time in his War incarnation, refused to see this and stole the super-weapon known as the Moment and 'destroyed' Gallifrey. However, the weapon, which was a living consciousness, convinced him to him to spare his people and planet, by showing him his Tenth and Eleventh incarnations and how what he would do would affect them. Agreeing with it, the Doctor teamed up with twelve of his other regenerations and placed Gallifrey and the Time Lords in a pocket universe to keep them safe and stop the Time War for good.
The Doctor forgot the events of what he had done until his Eleventh incarnation (twelfth face but thirteenth body). After these events, he would go searching for Gallifrey, coming close near the end of his Eleventh incarnation.
In the ModEdit
The Time Lords have appeared in the mod since November 2013, in what is called the 50th Anniversary Update. In the mod, their name is spelt 'Timelord' instead of 'Time Lord'. They are also hostile, though are planned to be changed to a neutral mob in the future. The Time Lords will also be able to regenerate in future updates.