Q: “I didn’t read Wikipedia. Who is the Doctor?”
A: The Doctor is an alien called a Time Lord. He is currently 900-something years old and travels about time and space in his ship, the TARDIS.
Q: “What the heck is the TARDIS?”
A: Standing for "Time and Relative Dimensions in Space", the TARDIS is the Doctor’s method of transport. It takes on the form of a blue police box and is bigger on the inside than the out.
Q: “Who are the people that the Doctor travels with?”
A: They’re referred to (usually by the fandom and the press) as his “companions”. Most companions are humans from Earth who get caught up in something the Doctor does and he takes them along on adventures.
Q: “Why are there numbers referring to the Doctor?”
A: Part of the Doctor’s abilities as a Time Lord is the power to basically cheat death through a process called regeneration. Any time his body is fatally injured, his cells can repair themselves, but it changes his appearance (and his personality) in the process. To date there have been eleven actors to play the Doctor in the canon of the series, and so, a number refers to what ever actor is playing the Doctor. (Keep in mind that no matter how much he changes, he is still the Doctor, retaining all his memories and basic traits throughout the years.)
Q: “What does it mean when somebody refers to “Classic” Doctor Who versus “New”?
A: The term “Classic” refers to Doctor Who’s original television run from 1963 to 1989 and the 1996 TV movie, which encompasses Doctors 1-8. “New” refers to the reboot of the television series that began in 2005 and so far encompasses Doctors 9-11.
Q: “What’s the long answer for telling people to start with Season 5?”
A: Season 1 is a good start, but a lot of the stories are hit or miss and it’s not the greatest way to sell a series to somebody who is probably expecting a good payoff from all the hype and love I and fellow Whovians have put into the show. Season 1 feeds into the next three, and although you can enjoy them without having viewed the previous seasons, you’ll still have dangling plot threads and be wondering why such-and-such is important.