When I was studying at York, reading the plays was part of the curriculum, and then, in the summer, there were a selection of the plays performed in the street (perhaps 15?), conveniently available to watch. Now that I am at Toronto, there are still medieval play recreations regularly available to watch, since the PLS is alive and well. The scholarly study of medieval drama has improved substantially since those early days, as Prof. Klausner made particularly clear in the Vagantes talk. REED, of course, has been a major contributor to the information available on the performance of medieval drama.
The York Mystery Plays were intended to be performed on Corpus Christi day, a day celebrated in honor of the Eucharist. Corpus Christi was established in England in the 1320s. Corpus Christi Day is the first Thursday after Trinity Sunday - which makes today Corpus Christi Day.
In honor of this, you could watch the video history of the modern recreation of the plays, which is available on the York Mystery Plays website. Another good piece of information on the way in which the plays work is available in the form of the Pageant Simulator, which, inspired by a U of T class with Alexandra Johnston (who is director of the REED project), simulates the relative lengths and progressions of the entire cycle of plays through the streets of York. It really does require a very full day to work through the entire cycle.
(Thanks to Denis G. Jerz for suggesting I mention Corpus Christi Day, and to curtana, whose incipient job inspired me to put a little more effort into the post than I might have otherwise.)