On the arbiter’s table at every open there is a thin book that nobody reads until something goes wrong. It is the FIDE Handbook, and everything that happens in the hall comes out of it: the two minutes your opponent gets for an illegal move, the shape of the pairings, the rating you go home with.
The name and the year
FIDE is the Fédération Internationale des Échecs, French for the International Chess Federation, and everyone says it as one word, fee-day. Delegates founded it in Paris on 20 July 1924, at the end of a large international team event held while the Olympic Games were in the same city. Its motto from that day has been Gens una sumus: we are one people.
The offices are in Lausanne, Switzerland. Around two hundred national federations are members, and the International Olympic Committee recognises FIDE as the governing body of chess, which is why chess keeps turning up in conversations about the Olympic programme.
The Laws of Chess, and how far they reach
Section E of the Handbook is the part you will actually meet. Article 4 is touch move, Article 6 is the clock, Article 7 covers irregularities including illegal moves, Article 9 covers draws and the threefold and fifty-move claims, Article 11 is conduct, and Article 12 is what the arbiter may do about you.
The preface to the Laws says something sensible that beginners never expect from a rulebook: the text cannot cover every situation that can arise on a board, so where a case is not written down the arbiter has to decide by analogy with cases that are. Chess rules are not a program. They are a short document plus a trained human.
Ratings, titles and an ID number
The rating list is published monthly, and it holds a standard, rapid and blitz rating for every registered player. FIDE also awards the titles for life (GM at 2500 plus norms, IM at 2400, FM at 2300, CM at 2200, plus the women’s titles), licenses arbiters and trainers, keeps the anti-cheating regulations, and organises the world championship cycle, the Olympiad every two years, the World Cup and the age-group championships.
There is a page here on the titles and one on how the rating arithmetic works, because those two are what most players mean when they say FIDE.
Your federation is the part you meet
You do not join FIDE. You join the national federation where you live, it registers you, and you get a FIDE ID that follows you through every event and every country for the rest of your playing life. The federation runs the domestic calendar, sends the results of rated events to FIDE, trains the arbiters and picks the Olympiad team.
Look up your own ID once, before your first rated event, and check that your name is spelt the way you want it spelt on a wall chart for the next thirty years.