This was a twelve-part serial, first broadcast between 13th November 1965 - 29th February 1966. The serial was written by Terry Nation and Dennis Spooner, produced by John Wiles and directed by Douglas Camfield. The script editor was Donald Tosh.
What I've seen:
Parts two, five and ten. As far as we know now, the other episodes were lost.
Since the three surviving episodes are more or less incomprehensible without some knowledge of the story, I'm going to discuss the plot in considerably more detail than usual.
At the start of part two the Doctor, companions Steven and Katarina and space security agent Bret Vyon, their temporary ally, are in the jungle on the planet Kembel. They can't get to the Tardis, since this is surrounded by Daleks. When the Daleks set the jungle on fire, they seek refuge in the planet's main city. There they learn that the Daleks have built an ultimate weapon, the time destructor, and that Mavic Chen, guardian of the solar system and leader of all humans, is in league with the Daleks. The Doctor manages to steal the taranium core of the time destructor, thus disrupting the Daleks' plans.
In the now missing parts three and four our heroes are chased by the Daleks and Mavic Chen's minions. Mavic Chen sends Sarah Kingdom, another space security agent and Bret Vyon's sister, after the fugitives. She kills her brother at the end of part four. Katarina is also killed in part four.
In part five the Doctor, Steven and Sarah Kingdom, who is still in hot pursuit, find themselves in the middle of a scientific experiment and are accidentally transported to a far-away planet, together with some white mice. They're menaced by invisible dinosaurs and eventually captured by the omnipresent Daleks, who also exterminate the mice. (Boo. Hiss.)
Between the end of part five and the beginning of part ten our heroes presumably escape, followed by more chasing. At some point the Meddling Monk, another Time Lord and the villain of an earlier serial, joins the fray.
In part ten the Tardis crew are in ancient Egypt, as are Mavic Chen, the Meddling Monk and, yes, more Daleks. Chen and the Daleks take Steven and Sarah hostage, and get the Doctor to hand over the taranium core in exchange for their release. The Doctor steals a component from the Meddling Monk's Tardis that he needs to mend his own, and tricks Chen and the Daleks into pursuing the Meddling Monk. The Doctor, Steven and Sarah set course for Kembel to thwart the Daleks' plans.
Eventually the Doctor vanquishes the Daleks by turning their own time destructor against them, but Sarah Kingdom is killed in the process.
The good news:
The not so good news:
If you're a hard-core fan, you'll want to see this. If not, it may not be worth your time.