The precise definition of folklore is a matter of some debate among those who study it, not least because the origins of the discipline very quickly tied the definition to some assumptions which have since been seen to be incorrect. One good modern definition is that it is the study of cultural expressions which are traditional and learned informally. By this standard, folk music is of a different sort from classical music not because it differs in any musicological way - though in the modern era it certainly tends to - but because of how it is transmitted. (One could argue that many of the novel compositions heard within the modern folk revival scene are more accurately folk-inspired rather than genuine folk music.) Folk tales are passed on through the generations and change as they go, as opposed to the consciously artistic presentation of a novel, which is kept and read in its original form.
Folk culture is often collected in rural areas, which often preserve traditional culture for a longer period than cities do. This has led to the assumption that folk culture is a rural phenomenon; on the contrary, it turns out that most elements of folklore which can be traced back to their origin began in cities and towns. Because a greater degree of formal education is often given to the wealthy, folklore is usually described as being of the common people, but in fact the upper classes have their own folk customs as well. (To pick a medieval example, there's no set-in-stone list of rules for courtly love that anybody was ever formally schooled in.) Folklore is also often described as oral, but in literate societies it spreads with no loss of authenticity through a combination of oral and written sources. In fact, it's often difficult or impossible to tell which changes in a given ballad family come from the publishers of broadsheets and which arise in the oral tradition and are embraced by the written versions; similarly, many fairy tales are passed on today in written and rewritten forms, but as long as they continue to be rewritten based on the tellers' recollections of what they see as central to the tale, they stay alive within a living tradition.
Folklore is also often imagined to preserve older ways and customs, and to some extent this is true, but it is always a mistake to suppose that a folk custom of one era accurately reflects its predecessor from a previous time. It is in the nature of informal transmission for things to change, keeping much of the nature of the most recent version while innovating whatever seems most relevant to the present. Thus, in the legends surrounding King Arthur, over time Sir Kay became a fairly minor figure while Sir Lancelot (a twelfth-century introduction to the legend) became prominent and central, to the point where even those with no interest in the Middle Ages know his name as iconic of knighthood to this very day. To pick a modern example, the Abbots Bromley Horn Dance described by Cecil Sharp in 1913 is still being danced to this day, and nobody can remember ever changing how they do it, yet in a mere century it is already recognizably different from the way Sharp saw it done. On the other hand, it's certainly a continuation of a very old tradition - there is a 16th-century reference which fails to mention the antlers seen as central to the dance in its modern form, and the antlers themselves have been carbon-dated to the eleventh century.
When folk customs cease to be a living tradition and become ossified and unchanging, they become much easier to study, but they also become far less vibrant and lose their place within the community. For this reason many modern sword and morris dancers will preface their dance notations with something along the lines of, "This is how we did this dance as of the year such-and-such, and should not be taken as a prescription for how to perform it now." This necessarily clashes with the desire to study historical folk customs in their historical context, however, as it is only when folklore is given a fixed form that we can be certain what it entails. Consequently, many of our sources for historical folklore studies consist of offhand references to a custom that is not explained in all its details. When a thorough description is given, we tend to assume it is of a quite typical example of whatever song, story, or custom it represents, which is a reasonable presumption when no compelling contrary evidence is presented but is not reliably accurate. Thus, for example, I tend to assume that Juan Luis Vives' Valencian ball game is typical of European handball in his era, despite having no earlier citations than his dialogue which even hint at anything like the laying of chases in court tennis, simply because there is little else to go on. If that rule is not in place in other related games, I don't know what is reasonable to use in its place (though there are several plausible guesses).
That said, I am of the opinion that these difficulties make the study of historical folk culture more engrossing for those willing to dive in, as it allows us a glimpse, however small, of the everyday life people led in bygone eras.