If we are talking about European history from the fall of the Western Roman Empire—and the simultaneous rise of the Byzantine/Ottoman Empire (476 cde) to the beginning of the Renaissance (1400 ce), the four best books I’ve ever read on the subject were:
(1) The Civilization of the Middle Ages, by Norman Cantor. This gives you a how and why things developed politically, economically and socially. It’s good, but a bit dry.
(2) The Barbarian Conversion: From Paganism to Christianity, by Richard Fletcher. The subject is about how and why we developed as Christians, with the most interesting historic anectdotes concerning the Church and it’s leaders including the Crusades and he impact they had on the populace.
(3) Barbara Tuchman’s A Distant Mirror which covers developments leading up to and surrounding 14th century Europe and the effects it had on the daily lives of members of each class. It includes the plagues, the economy, the cultures. It is my number one favorite book on the period. All of Tuchmann’s books were great. She was a fine historian. This is my all-time favorite book on the period and I really wish I’d read the first two listed here first—or at least The Complete Idiot’s Guide to the Middle Ages first.
(4) Medieval Lives, by Terry Jones and Alan Ereira. It’s about the people of the period. Cultural and social history of he times.
The best intro to the subject is of course The Complete Idiot’s guide to the Middle Ages. It will familiarize you with the seminal events of the period and save you time in later research.
An excellent book to have around while you’re reading the others is The Medieval World: An Illustrated Atlas
Note: I just saw @jaytkay‘s reference to Manchester’s book. I haven’t read it, but anything I ever read by William Manchester was gripping and impeccably researched.