This is sort of an ironic way of phrasing the question, since the Middle Ages themselves covered far more time than we often give them credit for, but any and all points along the Middle Ages and into the renaissance I would be interested in.
How did they view the past in chronological terms? Did they know how long Rome was around, how old the Greek civilization was, or that the heyday of ancient Egypt was thousands of years ago? Or did they think kinda like "dinosaurs and cavemen lived together", with all these ancient and long separated eras existing simultaneously or one after another?
Medieval scholars were well aware of chronology, since they had to calculate calendars so that they could accurately plot out the date of moveable Christian feast days like Easter (the subject was called computus). This science allowed them to produce tables which would show the date of Easter years in advance.
The development of Easter tables was the principle factor leading to the redating of time to the birth of Christ (Anno Domini, “In the Year of Our Lord’s [Incarnation]”). This was first calculated by the monk Dionysius Exiguus (Dennis the Short) in the sixth century but not widely used until popularized by Bede (died 735), a scholar in Northern England who was both an expert in computus and widely read throughout the continent for his biblical commentaries and other religious works (though known today mostly for his History of the English Church). Prior to this dating of years was usually carried out according to the year of the emperor or of the indiction cycle (a cycle of 15 years).
To the question about their knowledge of the past, they had access to a number of Roman and late antique histories of Rome. Perhaps the most popular in western Europe were Rufinus’s translation of Eusebius’s History of the Church, and, covering the earlier period, Orosius’s History against the Pagans (written after the sack of Rome to counter the pagan accusation that Rome suffered calamity because of punishment for abandoning the Roman gods and accepting Christianity). This history went back to the foundation of Rome and dated events according to how many years it happened from that founding date (which I think it set at 753 BC, though Orosius was writing before the use of AD and BC). There were plenty of other histories they also read, as well as chronicles, which listed all the important events that happened year by year.
Of course they also used the Bible as a source of history and took great pains to correlate the events it describes with contemporary events in Greece and Rome.
You can read more in The Oxford Companion to the Year by Blackburn and Holford-Stevens and in Faith Wallis’s book on Bede: The Reckoning of Time, and also in the primary sources like Bede’s History, Orosius, the Anglo-Saxon Chronicle, and others.