Just make sure you have a good sofa to hide behind when the monsters appear.
The great thing about DW is that you don’t need to know anything to get into the vast majority of stories. Since the series was revived in 2005, each year’s series [=US “season”] has had an arc, but even then many of the episodes function quite happily as standalone stories. Stories from past decades tend to be even more standalone.
It’s worth noting that as well as different settings, each story will often be very different in tone from the one before, and the one after it. There’s also probably more variety of tone within a story/episode than you may be used to. So if you watch one and don’t like it, or even hate it, it doesn’t necessarily follow that you won’t like or will hate the series as a whole.
The basic idea of the series is that there’s an alien, known as “the Doctor”, who travels in time and space in a blue box that’s bigger on the inside than on the outside. He usually travels with one or more “companions”, the vast majority of whom seem to be non-ugly lasses from Earth (Britain)! 
He has adventures. He fights wrongs.
That’s all you need to know! 