Hey! I can answer this one!

I am reading "The Calendar from David Ewing Duncan" and he makes it pretty clear that a normal person in the Middle Ages didn't really care about the year.

At that moment in time, people remembered days not as absolute points in a calendar but rather as Saint's Day.

That way, they knew to plan X on St-[saint name] day, and to plow on Ste-[saint name], etc...

But they didn't care about which year they were in. Season, yes, year, not so much because it had little influence on them.

Follow up question, would people have a sense for how old things were? For example, if a structure was over 1000 years old as opposed to hundreds, would they generally know (within an order of magnitude)?

On that note, does anyone know when the year 1 was decided to be year 1?

This question should be divided into consideration of rural and urban dwellers.

An average "normal person" from a medieval city, that is, a minor tradesman, merchant or hired worker, would have at least general idea which year it was, since various contracts, debts, loans, house-books of various guilds, and city-hall records were marked with exact dates. This means that various city clerks and merchants would keep exact measure of time, and the common men who traded/worked with them had to comply, and it was their responsibility to remember the date when they took a loan, or when their masterpiece is due.

I'm taking astronomy now and one thing I've learned is that from a very early age of man, we've used stars to find the changes of the days, months, years. People would travel great areas and teach others of the gods in the sky and of the coming seasons.