Basically what the title says. Would your average serf in Portugal or Spain or England have known what the americas were at the time of their discovery by Europe? How about in non-colonizing countries like Austria, or even further out in Poland or Russia? If not, when did their existence become widespread knowledge?
This depends on what you mean by "what the americas were at the time of their discovery by Europe".
Which discovery? Presumably you mean the one by Columbus and not the Norse explorers from centuries prior?
European expansion into the New World after Columbus was very quick (England, Spain, and Portugal all had expeditions before the turn of the 16th century, and colonies soon thereafter), so it's reasonable to believe that most people were at least vaguely aware that a new place, which at least by 1507 was already being called America, was out there. Did those same people know that this new place was the giant set of continents that they actually are? No, they didn't, because no one really did. It would be several decades before anything close to an accurate understanding of the size of the Americas was fully understood by any Europeans, let alone this knowledge being general information among peasants.
Magellan's crew first circumnavigated the globe in 1519-1522, a full thirty years (or a generation) after Columbus's voyage. Although Spanish explorers had crossed Panama and seen the Pacific almost a decade before that (in 1513), fuller exploration of the west cost of the United States didn't come until 1542 with Ferrelo, who sailed as far north as Oregon. The Spanish didn't reach Alaska until the late 18th century, when they used their supposed primacy via the Treaty of Tordesillas in their claim against the Russians they found already there.
I only know about Spain, so I'm limiting the answer to it.
First, there were very few serfs in Spain at that time, mostly limited to Catalonia.
Yes, the peasants were aware of the discovery of new lands from the very beginning, settlers arrived in the second voyage of Columbus. Peter Boyd-Bowman found records of at least 13262 people for the period between 1520-1539, illegal immigration and lost records may put that number over 100000.
But the most interesting thing about those figures is not the numbers, but the origin of the people. Most of them came from Andalucía, Extremadura and the Basque country, the poorest regions of Spain at that time.
And to be fair, even for peasants in the most remote places it would be pretty much impossible to ignore the huge impact the discovery of America had. Impoverished nobility left Spain for the Americas to become "conquistadores", felons could be deported to these strange new lands, trade and taxes became more regulated, etc...