Doctor Who: The Newbies Guide
This is the third story in Season 20.
The Fifth Doctor is physically younger than his previous incarnations. He wears Edwardian cricketing clothes with a stick of celery on the lapel. He is less eccentric than his previous incarnations. In Earthshock he was unable to save his companion Adric from dying.
Nyssa of Traken is the daughter of Tremas of Traken. In The Keeper of Traken she helped the Doctor and Adric to defeat the Melkur, a living statue that threatened their planet. The Melkur was actually the Master's TARDIS, and at the end of that story the Master took over her father's body. In Logopolis, the Master destroyed a large portion of the universe, including Traken.
Tegan Jovanka is an Australian air stewardess who accidentally stumbled into the TARDIS in Logopolis. She has a tendency to moan. In Time-Flight she was left behind in her native time, but in Arc of Infinity she happened to run into the Doctor and rejoined him on his travels.
Vislor Turlough is a new character who we are introduced to in this story.
Recurring and Historical Characters
Alistair Gordon Lethbridge-Stewart was the commanding officer of the United Nations Intelligence Taskforce (UNIT). He worked with the Second Doctor to defeat threats to Earth on two occasions (in The Web of Fear and The Invasion.) In Spearhead from Space, he teamed up with the Third Doctor to prevent an invasion by the Nestene and the Autons. During that story he persuaded the Doctor to work as his scientific adviser. He worked with the third Doctor for many years and witnessed his regeneration into the fourth Doctor. He subsequently worked with the fourth Doctor on a couple of different occasions.
The Black Guardian is a cosmic entity, being the equal and opposite to the White Guardian. In The Armageddon Factor the Doctor prevented him from getting his hands on the Key to Time.
It is not necessary to know any more than detailed in the summaries above,but you will appreciate this story better if you have seen The Armageddon Factor (for the Doctor's previous encounter with the Black Guardian) and at least a couple of previous stories featuring the Brigadier.