Do I need to play The Darkness to understand what's happening in The Darkness II, Or is it as easy as reading up on the plot?
Is highly recommendable to play the first game before. You will comprehend and appreciate better the second one. You will know the characters, the world, and so on. Besides, Darkness 1 is a very nice game and you will enjoy it.
But is not necessary: At the beginning of the Darkness II you have a really complete prologue that will tell you all you need to know.