How does Chaucer use irony in the Canterbury Tales?

There are numerous examples of dramatic irony in The Canterbury Tales. Overall, Chaucer skillfully uses irony as a way of putting distance between what appears on the surface to be the case and what he thinks is really going on. Right from the outset, Chaucer adopts the literary strategy of drawing a clear distinction between Chaucer the (somewhat naive) pilgrim, the narrator of the Tales, and Chaucer the author of those very same Tales, a world-weary, cynical chronicler of human foibles, forever casting a knowing wink at the reader.
The pervading sense of irony is much in evidence in The General Prologue. Here, we are treated to a collection of character sketches of each individual pilgrim that develops Chaucer's taste for irony to its fullest extent. Chaucer, the naive pilgrim narrator has, it appears, many a good word to say about his fellow pilgrims as they gather together at The Tabard Inn. However, upon on closer inspection, we find that things are not all that they seem. The monk, for example, is lauded as "A manly man, to been an abbot able." On a superficial level, this is high praise indeed. However, Chaucer the ironist arguably wants to suggest, ever so gently, that worldliness (rather than piety) is the ideal qualification for becoming an abbot.
This is one of many examples of Chaucer using irony as a means of satirizing the Church. Here we see that there is a serious side to Chaucer's use of irony. Though a devout Christian, Chaucer nonetheless subscribed to a widely-held conviction in the Middle Ages that the Church was irredeemably worldly, hypocritical, and corrupt. Irony in The Canterbury Tales is not simply used for comic effect; it has a clear moral purpose too.
Both comic and moral elements are ably combined in the amply proportioned figure of the Prioress. Chaucer the naive pilgrim gazes admiringly at her flashy jewels, including a "brooch of ful gold shene." Yet, Chaucer the ironist cannot resist insinuating that such ostentatious displays of wealth are rather inappropriate for the head of a nunnery.
Chaucer's irony, though, is never intended to be wounding or vicious. Even the Prioress, for all her obvious faults, still proves to be an immensely stimulating companion on the long, arduous journey to Canterbury. In other words, for all its importance as a literary device, irony is never allowed by Chaucer to obscure his unforgettable, sympathetic portrait of fallen humanity in all its richness and diversity.