How well connected were disparate Jewish communities in Europe in the Middle Ages and how did they communicate with each other?

They were plenty connected! A major source of employment for Medieval Jews was trading. Jews would travel long distances to trade various goods, sometimes for long periods of time. These trade networks spanned huge distances. One of the best records of Medieval Jewish trade is in the documents of the Cairo Genizah, which documents Jewish traders going as far as India, as well as correspondence between communities much closer than that about all sorts of community issues and trade.

Sadly, documentation of this sort is rather sparse. We don't have such fantastic document caches from most communities. What we do have an abundance of are letters sent between communities and Rabbis, asking questions about proper Jewish practice. What's more, younger students seeking education would travel to get religious education from a prominent Rabbi's school, which would help to disseminate that Rabbi's teachings and rulings through his students.

Anyway, on to those letters. They're usually a Q&A style format, where a question is sent to a Rabbi, sometimes at great distance, and he responds. These responses could be further copied and spread out for reference. In terms of how they communicated, the language varies. Often it was Hebrew, which was the common language of Jews internationally. There's quite a lot of written material in it. Other times it'd be Judeo-Arabic, such as Maimonides' letters with the Arabic-speaking world.

So, lots of connections, both in economic things and academia. There would be people traveling for both purposes, and letters getting sent around, some of which we're lucky enough to have today.

Sources:

Aust, Cornelia. “Between Amsterdam and Warsaw: Commercial Networks of the Ashkenazic Mercantile Elite in Central Europe.” Jewish History 27.1 (2013): 41–71.
Chazan, Robert. Reassessing Jewish Life in Medieval Europe. New York: Cambridge University Press, 2010.
Goitein, Shelomo Dov, and Mordechai Akiva Friedman. India Traders of the Middle Ages Documents from the Cairo Geniza: India Book. Leiden; Boston: Brill, 2008.
Hecht, Neil S., ed. An Introduction to the History and Sources of Jewish Law. Oxford : New York: Clarendon Press ; Oxford University Press, 1996. Print. Publication / the Institute of Jewish Law, Boston University School of Law no. 22.
Woolf, Jeffrey R. “French Halakhic Tradition in the Late Middle Ages.” Jewish History 27.1 (2013): 1–20.