Think back to the 1990s. "Return of the Jedi" came out in the 1980s. "Star Wars" fans didn’t expect there to be any more movies, weather prequels or sequels. So without movies, fans got the next best thing-books. Spanning from 25 thousand in-Universe years before Luke blew up the Death Star to 45 years afterwards, the Star Wars novels painted a cohesive story of what the Galaxy would have been like. It attempted to incorporate the prequel films into it, before it was erased form the continuity with the advent of "Force Awakens." Even those the events of these novels didn’t happen in the current "Star Wars" Universe, they’re still awesome things to talk about and read.
See, the old Star Wars Books-everything written up to a few years before "The Force Awakens," is placed into the “Legends” continuity. Since there are literally dozens of books, I’m going to to spend my time telling you the best ways to tackle them. There are no where near as many canon books, so you can pretty much just pick one up and read them.
Most of these books only require a basic knowledge of the movies in order to understand them. The first step is to watch the movies, and I’m guessing that if you clicked on this article you’ve already done that. The second step is to familiarize yourself with a handful of basic facts. Star Wars Books use Star Wars lingo. Instead of concrete and steel, they use Duracrete and Durasteel. That sort of stuff is pretty easy to understand, but what’s harder is that the books will often refer to races and planets without any explanation of what they are.
But you don’t need to know everything. You can use Wookieepedia to look up anything and everything you don’t know. Be wary of spoilers, of course, but there are some things you should know going in. There are several basic species-Ithorians, Rodians, and Twi’leks, to name a few-that are commonly refereed to throughout Star Wars Books. Knowing what these races look like and their basic history is very beneficial to understanding these books. And besides that, the lore behind these races can be fairly interesting. Be ready to look up any species that you haven’t heard of.
Here's a link to Wookieepedia's timeline of "Star Wars" books
BBY and ABY refer to years before and after the Battle of Yavin, which took place at the end of "A New Hope."
Glancing over this list, you can already tell that there are a lot of series. These books obviously build on each other, so they should be read in order. It is also notable that some of these books, namely the "Jedi Apprentice" and the "Jedi Quest" series, are meant for young children, so they might be boring to older audiences. Taking a glance over each book's description before you read it can let you know weather to book has ties to any other video games or novels, or weather you can pick up the book and enjoy it.
When you start reading books after "Return of the Jedi," (starting after four ABY) they build upon each other much more than the books set before and in-between the movies. Instead of building upon the events of the movies, they work off of each other. Starting with "The Courtship of Princess Leia" and continuing on in "The Thrawn Trilogy," the story of Luke, Leia, and Han's lives after "Return of the Jedi."
The trouble from here is that there are dozens of books in the post-"Return of the Jedi" era. It's highly unlikely that your local library will have all of them, or that you'll want to buy all of them. You can really get buy just reading the Timothy Zahn's books, as they are the best written and have the most continuity. Then we come to the "New Jedi Order" series, which details the Yuuzhan Vong war. The war itself is pretty awesome, it's just very hard to read through the entire seires and understand the continuity. From there, the Legacy series also follows a similar continuity.
Much to learn, you still have, but this should be a good guide to getting you started. Remember, the Force will be with you. Always.