How educated were the clergy during the Medieval period?

Latin was indeed the lingua franca of the period, and very, very few people could read or write. There just wasn't a lot of reason to be able to do so; paper was not introduced to Europe until the 1200s, so before then if you wanted to write anything down you had to go through the painstaking process of creating a piece of vellum or parchment for what it was that you were doing, and get to work. Indeed, many medieval manuscripts we have today show signs of having other material which was once on it but which was scraped away (the parchment/vellum version of erasing); the material was so scarce that there were many instances in which it the material itself was considered more important than the information that was written on it.

One result of this was that reading and writing were considered two separate skills at this time. This sounds really strange to the modern reader, I am sure - how is it even possible to write without being able to read - but that's exactly the case. A great many medieval scribes simply had no idea what they were copying down and simply did it by rote.

Here is a pretty decent discussion of why it is that we are all but positive these folks had no idea what they were writing:

A number of factors suggests that certain scribes who were engaged in copyist work in the first seven centuries or so of the Christian era were trained in a very mechanistic form of writing. The use of continuous script, without word breaks, suggests a very mechanical, letter by letter, approach to copying. Petrucci (Petrucci 1995) goes so far as to suggest that such works were copies for the sake of copying, rather than works for proper reading, and that some of the scribes selected for this work were actually the less intellectually able, who were trained in it as a mechanical skill.

He also claims that colophons by early scribes tend to refer only to the difficulty and tedium of the work involved, and contain prayers that this may help their eternal souls, rather than expressing pride in the product. Irregular letter forms which do not conform to any formal script type or house style, incorrect word spacing, bad Latin and a lack of appreciation of the graphic skills required to produce aesthetically pleasing letter forms are also indicative of the scribe with a purely mechanical, rather than literate, education.

Theoretically, the clergy were well educated. The first universities that went up in Paris and (I think) Brussels were erected to provide a broad-based clerical education that covered reading, writing, oratory, and logic. Before this and for centuries afterwards for that matter, the wealthier nobles hired tutors to come in and teach their kids. As many of the younger children of nobility ended up going into the church, this also added to the general level of education of "those who pray".

Because of alms and penances paid by guilty nobles, the church also became extremely wealthy (if memory serves, for example, William the Conqueror paid the church to pray for him for such a long period of time that if a single person was doing the prayers and was immortal or something, they'd still be praying today). This led to there being an upper crust of clergy who didn't actually do a whole lot and a whole lower class of "lay clergy" who, essentially, did all the grunt work. Every now and then some local scandal would erupt when it was found that these lay clergy had all the education of, well, peasants, since that's what they were.

So the long and short of it is: the higher-ups were generally as well educated as anyone at the time, but as you got further and further down the pecking order, literacy was not even a given.