Lonely Swordsman said:
Don't.
I've been trying hard to get into Doctor Who and it's just not possible. Every single time I start warming up towards the show it does something incredibly stupid. Spare yourself the time, it will only aggrevate you.
You definitely can't take Doctor Who too seriously.
If you've got a Sci-Fi scale where one end has a focus on storytelling, with Science as a tool to get you to intersting places and events, and on the other end, you have stories exploring the implications of a very real and factually accurate technology/science. Well, Doctor Who is so far down the storytelling end, it's often been described as modern Fairy Tales, with all the grim realities that pop up in such stories (innocents get eaten alive all the time in Fairy Tales after all).
I mean, depending on how you look at it, most scientists agree time-travel is Impossible, and never will be possible because that's not how time works. But as we know Doctor Who is a Time-Traveller, and it really goes from there. If you like your Sci-Fi to be logical, and make sense all the time, Doctor Who will only infuriate you, it's not for everyone. But as far as storytelling is concerned, the good Doctor will take you to more varied locations and situations than any other character in the history of Television.
I mean, who else do you know who's defeated Cyborgs, Romans and Satan (without using weapons)?