The Time Lords owe their existence to two solar engineers, Omega and Rassilon. Rassilon was acclaimed as a young hero when he destroyed the Giant Vampires with his bow ships (State of Decay), after which he and Omega collaborated on the ultimate defence system for Gallifrey, the living metal validium (Silver Nemesis). Rassilon had, for a long while, been frittering away his technological advancements on the construction of a time scoop (The Five Doctors), which could bring creatures from other times and worlds to Gallifrey. Only when Omega was brought into the picture did Rassilon perceive that together they could create fully functioning time travel craft.
Omega, a member of the High Council, journeyed into a sun going nova in order to provide his people with the energy needed for time travel (The Three Doctors). According to Remembrance of the Daleks, the supernova was created by a stellar manipulator (the Hand of Omega), which 'customises' stars.
('And didn't we have trouble with the prototype...' notes the Doctor, changing it to 'they' when Ace queries 'we'. [He might mean 'we' as in 'the Time Lords', or perhaps his first TARDIS trip was back to those times, forcing him to leave Gallifrey when he was given the hand for safe keeping. Since Susan came up with the names for TARDISes, perhaps she is from those older times, a young Gallifreyan from before the Time Lords could regenerate.])
Although Omega's mission was a success, he never returned, and much of the praise was heaped upon Rassilon. (So much so that, according to Four to Doomsday, his name is known even among races who haven't heard of Gallifrey. Omega, however, was always a hero to the Doctor.) Rassilon's mission was to journey into a Black Hole to find the Eye of Harmony (the 'nucleus' of the hole), which he then balanced against the mass of Gallifrey enabling Time Lords to 'neither flux, nor wither, nor change their state'. Rassilon was protected by his sash (which prevented him from 'being sucked into a parallel universe', as Omega was).
The successful outcome of both missions heralded the true dawn of the Time Lords, a move away from the Old Time (Silver Nemesis) and towards a new era of enlightened benevolence. However, one of their first acts was to encourage the development of the Minyans (Underworld), an intervention that was so disastrous that thereafter the Time Lords rulers vowed not to interfere with the affairs of other worlds.