Medieval preaching outside of clergy was in vernacular languages. Contrary to popular belief, the Roman Church of the middle ages did not restrict verbal preaching languages and in fact encouraged the oral dissemination of it, but through approved channels only: the ordained clergy, to ensure messages and interpretations were within orthodoxy.

We actually have copies of sermons called reportationes which:

are themselves sometimes ‘‘macaronic’’, a mixture of Latin and vernacular, reminds us of another problematic presented by written texts as a window on the preached word [...] A preacher moved from Latin texts, the Bible and his notes, to a vernacular preached word, which the reporter took down, usually in Latin shorthand. The reportatio itself could then be edited into more literary Latin to provide a final version. Sermon texts masque not only a motion from oral to written, but often another from one language to another. Recent studies have begun to explore the transition from Latin to vernacular, as reportatio studies did the transition from text to orality. The rich corpus of Italian sermons by Jordan of Pisa can be compared with his Latin sources and preaching tools. Similar work has also been done for late medieval England, where vernacular versions of extant Latin sermons and vernacular sermons dependent on Latin preaching tools allow similar analysis of the translation process. There, surprisingly, we find vernacular sermons that are more complex than their Latin models. [Carolyn Muessig et al, Preacher, Sermon and Audience in the Middle Ages (Brill, 2002)]

The above is in regards to the masses of reportationes found in urban archives in France, Italy, and England. However, by the 13th century village clerics would often receive training based on these sermon collections to spread the orthodox teachings among rural populations. It is possible that ritualized sacraments like eucharists were conducted in Latin, a kind of formula-based performance that would be understood by non-Latin speaking laity through reinforcement and repetition.

Also see the various works of Beverly Kienzle on this, one of the foremost scholars of medieval sermons.

Now, the question isn't whether the average western medieval subject understood what was said in church, the real question is how often did they go, and where else might they get their understanding of the bible? This is less understood, but is an undercurrent that draws me to study heresy and the medieval inquisition.

Mystery plays were another method for disseminating biblical stories to the laity. I don't have my sources on hand at the moment. Can anyone comment more fully on this medieval tradition?