First Doctor's renewal

Following his prevention of the 1986 Cyberman invasion of Earth, the First Doctor experienced a bodily renewal in which he became the Second Doctor; (TV: The Tenth Planet, The Power of the Daleks) the Doctor would later refer to this event as his reincarnation (PROSE: Only a Matter of Time) or his first regeneration. (PROSE: Timewyrm: Apocalypse, Christmas on a Rational Planet, World Game, et al.)

Nature
Immediately after its occurrence, the Second Doctor compared the renewal to a butterfly's metamorphosis, saying that "life depends on change -- and renewal." He claimed that his renewal was part of the TARDIS, necessary for his survival. (TV: The Power of the Daleks)

One account indicated the process a "strange psychological storm" which rejuvenated him but also overwhelmed him such that he almost became a new, younger personality. This was similar to the rejuvenation of a phoenix. (PROSE: The Phoenix in the TARDIS) The "rejuvenated Dr. Who", who thought of his prior body as his "older form", once explained to his companions that the closest term for the process would be "reincarnation". (PROSE: Only a Matter of Time)

Later sources indicate this was a "regeneration", a Time Lord biological process. (AUDIO: The Power of the Daleks, PROSE: Lungbarrow, et al.) By one account, there were many types of regeneration, with this being regenerative technique known as the "White Light". (PROSE: How to be a Time Lord) Other accounts indicate this regeneration has gold regeneration energy. (COMIC: Blood and Ice, TV: Twice Upon a Time)

The Doctor's prior experience with renewal
By many accounts, this was the Doctor's first regeneration. (TV: The Three Doctors, Twice Upon a Time, PROSE: Lungbarrow) However, the Doctor indicated he may have regenerated before. (PROSE: The Power of the Daleks)

Anticipation
While observing the Ashtallans on Ashtallah, the First Doctor pondered on the nature of his regeneration. (AUDIO: The Invention of Death)

Shortly after he met Katarina, the First Doctor began to feel he was nearing the end of his life. (PROSE: Scribbles in Chalk) Several months later, while in ancient Egypt, the hot weather bearing down on him caused him to consider that he was no longer as young as he once was, or "would be again". (PROSE: The Mutation of Time)

While contemplating his sacrifice to satisfy the Web of Time, the First Doctor reflected on regeneration, and the person he could become when he regenerated. (AUDIO: Men of War)

Weariness
After his struggle with the Celestial Toymaker, the First Doctor became increasingly unwell from fatigue, (PROSE: The Man in the Velvet Mask) and was aware his loss of strength would lead to his regeneration, something he was afraid of. (PROSE: Ten Little Aliens) After he was joined in his travels by Ben Jackson and Polly Wright, (TV: The Smugglers) the First Doctor was aware that his regeneration was nearing. (PROSE: Ten Little Aliens, Five Card Draw) Throughout all this time, however, he resisted and suppressed the regeneration process. (PROSE: Twice Upon a Time)

By the time the First Doctor, Ben, and Polly arrived at Snowcap Base, the Doctor had been suffering intermittent moments of delirium, sometimes referring to Ben as "Ian" and Polly as "Barbara", much to their confusion. (PROSE: Doctor Who and the Tenth Planet)

Encounter with the Cybermen
The Doctor collapsed when Mondas began draining Earth's energies, (TV: The Tenth Planet) due to his regeneration process starting, (PROSE: Interference - Book Two) and Mondas syphoning off his ability to resist regenerating any longer. (PROSE: Twice Upon a Time)

While emerging from his sleep, the Doctor overheard Ben claim that it was "all over now," and became weary. (TV: The Tenth Planet) Walking in the snow, the Doctor caught a fading image of Oliver Harper. (AUDIO: The First Wave)

Rejection of change
By some accounts, after his regeneration started, the Doctor rejected it. Walking through the snow, he insisted to himself that he would not change and that the entire idea was "ridiculous." (TV: The Doctor Falls) However, he became involved in the Twelfth Doctor's regeneration and was inspired to regenerate.

Now inside the TARDIS and glowing with more regeneration energy, the Doctor managed to set the coordinates to return it to Antarctica in 1986 (TV: Twice Upon a Time) using the fast return switch. (PROSE: Twice Upon a Time)

The renewal
As the TARDIS' controls continued to operate on their own, the Doctor opened the doors for Ben and Polly before collapsing unconscious to the floor, having lost the energy needed to keep his old body going. Before the astonished eyes of his friends, the Doctor regenerated for the first time, transforming into a much younger man. (TV: The Tenth Planet)

The Second Doctor saw his first incarnation in his reflection while still adjusting to his new body shortly after his first regeneration. (TV: The Power of the Daleks)

Aftermath
Immediately after his first regeneration, the Doctor was at one of the weakest points in his life, allowing the Timewyrm to enter his mind, where it would stay until he travelled to Panjistri with Ben and Polly. (PROSE:  Revelation)

After the renewal was completed, the new Doctor found himself suspected as an impostor by Ben, while Polly was more ready to believe that he was the same Doctor. He found that his signet ring no longer fit. (TV: The Power of the Daleks, COMIC: The Chameleon Factor) Very soon after, they all became caught up in events on the planet Vulcan. (TV: The Power of the Daleks)

Legacy
Upon coming back into contact with the Second Doctor, the War Chief revealed that he knew who he was despite his change in appearance. While ordering the Second Doctor's change of appearance at the end of the Doctor's trial, the First Time Lord noted that the Doctor had changed appearance before. (TV: The War Games)

The Seventh Doctor relived his memories of the First Doctor's regeneration while he was interrogated by Matheson Catcher. (PROSE: Christmas on a Rational Planet)

When the Doctor's friends travelled through the Seventh Doctor's memories, they experienced all seven of his previous regenerations, including the First Doctor's. (PROSE: Lungbarrow)

When the Twelfth Doctor visited Snowcap University, he was unnerved due to associating the area with his first regeneration. (COMIC: Blood and Ice)

The Doctor's age
By one account, the Doctor was 450 years old at this time. (PROSE: Iceberg) By another, he was 900. (PROSE: The Phoenix in the TARDIS)

Shortly after the regeneration, the Second Doctor told Ben Jackson and Polly Wright that it had been over 750 years since he left his home planet. (PROSE: The Power of the Daleks)

The First Doctor's regeneration happened roughly 1,500 years before the Twelfth Doctor's regeneration. (TV: Twice Upon a Time)

Behind the scenes
The earliest-known production office-generated document on the Doctor's renewal described it thusly: "The metaphysical change which takes place every 500 or so years is a horrifying experience — an experience in which he re-lives some of the most unendurable moments of his long life, including the galactic war [which was believed, at this time, to have been the cause of the Doctor and Susan's departure from their home planet]. It is as if he has had the LSD drug and instead of experiencing the kicks, he has the hell and dank horror which can be its effect."

- 1966 production note, entitled "The New Doctor Who", The Second Doctor Handbook p.24

Regeneration, an installment of the Reconstructions series, recreated the First Doctor's renewal using actors David Bradley and Reece Shearsmith, who played First Doctor actor William Hartnell and Second Doctor actor Patrick Troughton respectively in the docudrama An Adventure in Space and Time. Another Doctor added Mark Gatiss as the Third Doctor to the mix.