The quality of Medieval Latin can vary quite a bit…sometimes it’s pretty bad, but it’s mostly quite good. Some authors had mastered it and are basically indistinguishable from classical authors.

“Despite its richness and diversity and the excellence of much of its literature, Medieval Latin has often been dismissed, by austere classicists and others, as a debased form of Classical Latin—infima latinitas ("the lowest form of latinity," "kitchen Latin")—and a cloud of disparagement and prejudice has obscured its vital role in the transmission of Western culture.” (Mantello & Rigg, pg. 4)

First of all we should remember that Medieval Latin isn’t “vulgar” Latin - the everyday spoken Latin that wasn’t written down, and which evolved into the modern Romance languages. Medieval Latin is just Classical Latin, as spoken/written by people who learned it as a second language. Some learned it better than others, but everyone learned the same Classical Latin that ancient native Latin speakers learned. Medieval Latin developed a few different rules, sometimes the grammar is a bit different, and certainly the spelling and meaning of words changed sometimes too - but it’s definitely still meant to be the same Classical Latin that they learned in school.

Anyone who had some education and could read learned to read in Latin first, whatever other languages they might know. It might not be their first spoken language but it was their first, and for a long time maybe their only written language. Students learned from textbooks just like we do - some popular textbooks, which were used and copied throughout the Middle Ages, were the Ars grammatica by Aelius Donatus (4th century) and the Institutiones grammaticae of Priscian (6th century).

They also learned from classical literature, which was still widely available. Students read Caesar’s histories or Cicero’s letters, or poetry like the Aeneid, not too different from what students read today. More advanced students could read things like the plays of Plautus, or the letters of Seneca. Medieval scholars also created their own text books (an “ars dictamina”) with formulaic phrases that they could copy and reuse from ancient sources. Seneca’s letters, for example, were extremely influential on the way Latin letters and administrative documents were written.

Of course, as you mentioned, the other major source for medieval authors was the Latin translation of the Bible by St. Jerome in the 4th century (although there was also an older translation, the “vetus Latina”, which still had some influence). Jerome sometimes translated Greek and Hebrew phrases a bit too literally, into something that may have sounded strange and not quite like proper Latin in his own time. But since everyone who learned to read Latin also learned to read the Bible, some of the strange grammar and syntax of the Bible became good idiomatic Medieval Latin.

For example, if you’re familiar with Classical Latin you know about the “accusative infinitive” construction, i.e. instead of using a subordinate clause like we do in English and the modern Romance languages, Latin used an infinitive verb and an accusative object pronoun. We might say “I say that I am tired”, while a Classical Latin speaker would say “dico me fessum esse” (literally more like “I say myself to be tired”). It was possible, but rare, in Classical Latin to introduce a subordinate clause with “quod” or “quia” or even “quoniam”, and that’s what Jerome often did when translating the Greek and Hebrew of the Bible. In that case, “I say that I am tired” became “dico quod ego fessus sum”. This was probably how Vulgar Latin was spoken too, since it’s exactly the same construction we find in modern French, Spanish, Italian, etc. This construction was very common with medieval authors too, maybe because they were already used to speaking that way in their native languages. But they also knew how to use the accusative-infinitive construction, and you’ll often find both forms used by the same author.

“Most of the syntactic developments in Medieval Latin arise from the fact that all its users were, by birth, speakers of a vernacular language. While they might learn the inflections of Latin, their mental syntactic structures were English, French, German, Italian, and so on. Thus they frequently expressed themselves in structures that reflected their native habits, even when using Latin words and inflections.” (Mantello & Rigg, pg. 85-86)

Sometimes they might also use some unexpected spellings, probably based on the way people actually pronounced Latin at the time. For example “mihi” (“to me”) could be spelled “michi” because they pronounced the “h” more like the German “ch”. Words with “ae” or “oe” were often just spelled with an “e”. Sometimes you might see a “p” inserted in a word normally spelled with an “mn”, like “calumpnitas” instead of “calumnitas”.

The quality of the Latin also varies depending on when and where it was written. Latin from the end of the classical period/the early Middle Ages is sometimes very strange, but that was a time when Latin was still considered to be the first language everyone was speaking. We would now say they were speaking late Vulgar Latin or an early form of a Romance language, but they didn’t think so at the time. The idea that Latin was something different from what they were normally speaking didn’t develop until later in the Middle Ages (from the 9th century onwards). So if you’re reading something like Augustine of Hippo or Gregory of Tours, or administrative documents from Merovingian Gaul, it’s definitely Latin but it’s quite like Classical Latin and it’s not like the conscious imitation of Classical Latin from the later Middle Ages.

Anecdotally, I typically work on stuff from the 12th and 13th centuries, and I read a lot of good Latin written by well-educated people (papal letters, historical chronicles), as well as some not so great Latin written by less-educated writers (charters issued by a local aristocrat, documents written by notaries). If I’m reading a letter written in the papal chancery, I can expect the author to have the best training and very good mastery of Latin style. A papal letter might be several pages long with lots of fancy rhetorical tricks - my favourite example that we read in school was a letter where, in good Ciceronian style, the subject of the sentence and the subject’s main verb were separated by two pages of subordinate clauses.

Meanwhile, some local secular ruler probably doesn’t have a professional chancery like the pope, so a local monk or priest might be writing for him, but they don’t quite have the skill of the professionals working for the pope. And notaries, who were busy churning out lots of legal documents, might be copying from a book of examples, so their documents can be pretty repetitive and sometimes it seems like they don’t really understand what they’re writing.

And I haven’t even touched on the creativity of other kinds of literature and philosophy and poetry, but again, they followed the rules of Classical Latin while innovating wherever necessary. Classical poetry, for example, always followed specific metrical patterns, such as the dactylic hexameters of the Aeneid. The poetry comes from the flow of the meter. Medieval poets could master these patterns as well, but they also developed rhyme schemes! Rhyming Latin poetry is pretty great.

So it really depends on what you’re reading, who wrote it, and when, but for the most part it’s just Classical Latin with a few extra rules to learn. If you can read Classical Latin, you can quickly get used to Medieval Latin. Sometimes it will be simpler, but the best medieval authors are just as complex as the best classical authors.

“Cicero himself would have been able to read most Medieval Latin with little difficulty, once he had accustomed himself to a few differences in spelling and some new vocabulary” (Mantello & Rigg, pg. 73)

Sources:

F.A.C. Mantello and A.G. Rigg, eds., Medieval Latin: An Introduction and Bibliographical Guide (Catholic University of America Press, 1996)

John F. Collins, A Primer of Ecclesiastical Latin (Catholic University of America Press, 1985)

From what I know, language learning back then was also not very advanced and consisted mostly of reading the Bible and religious texts.

This is a real misconception. To start with, we have a very wide corpus of Medieval texts from a whole array of genres; yes, the Bible, Books of Hours, Psalters, Biblical commentary and theology, but also a wide variety of scientific treatises, medical textbooks, translations of Classical philosophy, herbology, histories and biographies. And most importantly, texts which suggest people read for entertainment and fun: poems, riddles and verse, Chansons de Geste, romances, epics, although these were often frequently in vernacular.

Jordan Fantosme's Chronicle of the War Between English and the Scots, 1173-1174, while a history, is also a pioneering work of insular French verse, written in rhythm and rhyme. Middle English texts like Chaucer's Canterbury Tales or Malory's Morte d'Arthur are texts clearly intended for recreational reading by a literate audience. Other genres, such as the large corpus of Chansons de Geste are written records of popular legends most usually performed aloud for a largely-illiterate audience.

Education in Latin literacy was started at an early age and could be a very important and intensive process. We have a relatively extensive corpus of surviving learning aids even from the Early Medieval period: practice tablets, Old English to Latin dictionaries and phrasebooks, etymologies and florelegia - collections of useful quotes and important excerpts from Classical or contemporary writers. Emphasis was put on consistency of style and legibility as much as on spelling. Fascinating marginalia from some surviving 10th Century phrasebooks in the British Library shows students scribbling in their own handwriting in the margins alongside the stylised formal writing of their practice sheets. This isn't to say that things were flawless at all: levels of learning and skill fluctuate from period and location and even from individual scribe to scribe. Alcuin of York famously expressed to Charlemagne a concern that some clergy in 8th Century Francia barely knew enough Latin to make it through the Mass, let alone to write properly. In contrast, the 15th Century London Lickpenny - often attributed to John Lydgate - makes reference to the wide array of literate and educated individuals one might find working jn the city, including legal clerks, treasury clerks, magistrates, judges, secretaries and merchants.