If you wish to get a taste of the typical quality of the stories here while still giving yourself the chance to read on if you like it, then read A Tenno's Kind of Espionage. If you want to back up a little to get more of the context of the events leading up to the start of that story, give Concerning Conspirations a quick read first.
If you want to dive into our feature timeline from the beginning, start at The Weaver's Manifest's Introduction and read up.
If you are fascinated by our story canon and want to read everything to see how far they came, start at The Tomb of Red Dust and read up.
Since the official year measurements are unclear in the game, our universe uses the climactic story of the Orokin Remnant as an inflection point to count years and months. [BR] counts time Before the Remnant, [DR] counts time During the Remnant (which lasts a total of about a year), and [AR] counts time After the Remnant. The format is month/day, so 3/2 is the 2nd day of the 3rd month.
Read about what the Orokin Remnant is on our history page here.