You could start by reading all Codex entries, and the game manual
https://www.elitedangerous.com/help/manual/
Plenty of Galnet news over the years, you can read them at
https://community.elitedangerous.com/en/galnet
Deeper knowledge of the world can be gained by visiting tourist beacons, and studying the Canonn website, preferably all entries there. There are collections of tourist beacon entries, for the comfortable explorer I would recommend video series by Brad Hann.
It gets a bit trickier here. Many fragmentary pieces of information you now have relate either to official Elite Dangerous books, list (partial?) of which you can find here
https://www.frontierstore.net/books.html
or past Elite games, notably Frontier: First Encounters. There are content inspired by fiction associated with older games too. Therefore, to understand Elite lore and history, it is worthwhile studying sources such as
http://wiki.alioth.net/index.php/Main_Page, FFE journals, ancient fan websites, novels, maybe Oolite included. Even manuals of the older games.
What you must here understand is, Elite Dangerous books are considered canon, but in reality they are narratives based in the game world, with some source material provided by Frontier, and some connection to content ingame. Material for other, older games however is not considered canon, but is set in the same universe, and this content is "echoed" in Elite Dangerous, in ways decided by Frontier.