This topic falls naturally into two sections, the Church and the Faith. The former is the history of an institution and concern the popes, the national churches, finance and administration, and power in general. Faith includes matters such as popular piety, theology, heresy, and the like. Both topics are especially rich during our era. You will notice that your authors tend to divide the material along these lines as well.
Much of the institutional history for this period concerns the papacy, and rightly so. Divide papal history into thirds: the Babylonian Captivity, the Great Schism (and the Conciliar Era that overlaps it), and the Renaissance popes. Each period had its own characteristics and preoocupations; again, the textbooks do a decent job on each section.
The Faith portion is covered less well—there's a limit on what will fit into a textbook!—and I will spend a bit more attention on that. In particular I address the basic tenets of faith (doctrine), the forms of formal worship, the wide variety of informal religious expression (often referred to as "popular religion"), and the boundaries of religious life (heresy being the most obvious example).
I characterize the entire period as exhibiting two trends that both conflicted with and reinforced each other. At the center of the Church I see failure. The popes failed in the 14th century to reform the Church and indeed were a significant source of corruption themselves. That failure became even more evident during the Great Schism. The Councils, too, failed to reform the Church. They even failed to unify the Church, though Constance did manage to return it to one pope, but that same Council failed to overcome the influence of the national churches. Finally, the papacy again failed later in the 15th century to address reform and the increasing nationalization of churches.
On the other hand, this was a period of tremendous spiritual vitality at the local level. A few names will have to suffice to indicate this: Brethren of the Common Life, the Hussites, the flagellants, Wycliffe, the Spiritual Franciscans, Savonarola, the Waldensians. What's striking is how much of this activity took place outside the Church, either indifferent to it or actively critical of it. People were searching for meaningful spiritual activity, but they were less and less inclined to look to Rome for leadership in this.
You should be mindful of these two themes as you read through the material. While two simple ideas cannot capture the religious life of an era, they can perhaps help you organize the material and help you make your own sense out of it.