The main thing you need when you read any of Austen's novels in general—and this one in particular—is a fine-toothed comb. (Not literally. Although who knows? Maybe you brush your hair while you read, and it's really not any of our business.) But you certainly need a metaphoric comb, because Pride and Prejudice depends on nuance. Every tiny turn of phrase, every slightly raised narratorial eyebrow, and every throwaway aside are crucial.
For example, check out the very first line: "It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife" (1.1). Major sarcasm alert, Shmoopers. Austen doesn't believe this At All, which you find out the next sentence, when we learn that a new single neighbor "is considered the rightful property of some one or other of [the local] daughters" (1.2).
That snide little "property" upends the typical relationship of in which the man has all the financial power and gives it to the woman and her family, who consider the man their "property." And hearing the sarcasm in that line lets you go back and reassess the first line, to realize that we're being set up for a whole novel that questions the standard quo attitudes toward marriage and money. But see how subtle it is? A summary doesn't really do it justice: Austen is one writer where form (the how) and content (the what) can't be separated. (Of course, we're still going to summarize it anyway. But you should definitely read it for yourself!)
Other than that, there are a few of the usual suspects when it comes to reading something written long ago and far away: (1) getting used to the different quantitative systems—money and distances are really different when you're pre-industrial revolution and pre-railway travel; (2) adjusting to the different social norms and values—back in the day, an unmarried woman is considered a parasitic waste of life, basically, so getting married is more about life or death than picking out a color scheme.