For historians, a year is generally a calendar year, it's not something that's super complicated. Obviously people around the world have used and continue to use dating systems that are not "Western," but there are a number of online resources to convert from different types of calendar into another.

How do you solve things when people used a slightly different calendar than we did? Let's say a letter written by someone living under the Orthodox Julian calendar, would you leave that date like it was, or would you calculate what date that day would have been in our calendar and if so which calendar? Also do you keep track of leap years when converting other calendars to the current one?

If you're dealing with a historical period when two countries use different calendars, for convenience, you generally would convert to one calendar system or another and explain this in a preface, foreword or notes. This happens more often than you'd think, even historians of World War II deal with the fact that dates in Japan are a day earlier than those in the U.S., due to the International Date Line. (That is, the Pearl Harbor attacks took place Dec. 8 in Japan.)

When we say that the US declaration of independence was written on the fourth of July in 1776, does that mean that the people back then would have called that day July the fourth, or that it is exactly 87 732 days ago (with days being 86 400 seconds long)?

Well, to be super pedantic, the Declaration was written in June 1776, it was just adopted on July 4. But people then would have called the day July 4 (it's on the document, after all) as the U.S. had adopted the Gregorian calendar in 1752.

You may also be interested in this section of our FAQ on calendars and dating.