Now, the obvious answer is "God created it in 6 days in about 4000 BC". But I've read that many classical and medieval theologians, such as Origen, St Augustine, Thomas Aquinus, etc, claimed that God created the world instantly, timelessly, or something like that, and that the 6 days were metaphorical in some sense. Though I know Martin Luther believed that it was literal. So, what I wonder is a)how your average peasant believed the world began, and b)what educated Catholics (or Orthodox) believed. Also, were there any significant changes to their understanding of the world's beginning prior to the Reformation, or did Church teaching stay pretty much the same throughout the whole medieval period?
I just thought that I'd add that Protestants didn't really exist in the Middle Ages, at least on a noticeable scale. At this point in time, they would have just been labeled heretics. Many people didn't even realize they were being heretics. Like /u/Kotoro7 mentioned, they often developed in geographical areas that didn't have the Church carefully overseeing and educating on Catholic beliefs.
However, I can add a bit to this. The Magisterium of the Catholic Church has actually never mandated a particular viewpoint that one was required to hold about the beginning of the world because it doesn't correlate, in the Church's eyes, to the salvation of an individuals soul. However, to not be heretical, certain things about creation did/do have to be believed. One had to believe that God created the Earth out of nothingness (that didn't mean no Big Bang/evolution or anything like that. It just meant that God brought material into existence. He could have used a variety of methods that one was allowed to believe), that at some point God gave humans personal, moral culpability for their actions, and that all human beings are born with original sin.
This is not to say that certain ideas weren't treated with preferential treatment throughout the history of Christianity. A careful examination of the fathers of the Christian faith will demonstrate that taking the Genesis account extremely literally was not too popular because taking it word for word would demonstrate a misunderstanding of the context it was written in. For example, the story of Noah's Ark is definitely a plagiarism of the Epic of Gilgamesh but this was done intentionally to help teach a moral lesson and provide an allegory to how the Earth came to be in it's current state with a story that people would have been familiar with and enjoyed. Thus, taking this story literally would have been seen as a bit silly by serious theologians.
One common view that I've encountered during the Middle Ages (and other periods of Christian history) was the idea that the six days of creation were not literal, but rather a literary device used by the writers of the Old Testament to place an emphasis on the seventh day: the Sabbath.
St. Augustine, a popular and influential medieval bishop/theologian/philosopher, believed that God created the world in one single instant and that the six days of creation were allegorical.
St. Justin Martyr, while not existing in medieval times, still had his writings studied in this time period. He proposed a type of old-earth creationism, believing that each day in the Genesis account took place over thousands of years.
St. Thomas Aquinas, another wildly influential medieval theologian/philosopher seems to hold the view that it was perfectly acceptable to view creation as a literal twenty-four hour day because scripture said that was what happened but didn't necessarily take that literally. As a fun fact, Aquinas actually had some leanings that suggested a belief in a sort of evolution - that God didn't create the world in it's current state all at once but that he allowed it develop over time. Use the word evolution loosely though, because it definitely wasn't a Darwinian understanding.
Like I said, there are many interpretations and in different areas some interpretations were more popular. Sometimes including heretical beliefs that had to be fought by dispatching monastic orders to an area to reprimand any heretical clergy and instill accurate and orthodox beliefs into the locals.
For a more in depth examination of similar, but different viewpoints, I'd recommend St. Augustine's Commentary on the Book of Genesis or On the Literal Meaning of Genesis and book two of St. Thomas Aquinas' Contra Gentiles or Treatise on Creation.
TL;DR: Your average peasant would have usually believed whatever the most prominent theologian in their area happened to be. Did the local priest have an affinity for Aquinas ? Good chance the local populous would have believed that way. Did the locals live in the area under Augustine's supervision? Likely the locals felt similarly to Augustine.
EDIT: This comment was originally written in response to a comment that has since been deleted. I hope it still makes sense. If not, I'd be glad to clarify any confusion! I also noticed I started rambling and tried to fix some of that, but again, will gladly clarify any confusion!