In the beginning there had to be only the great leaders and wealthy who "decided" how history would be recorded. How has it changed in modern times when the views and perspectives from minorities and new sources surface?
Probably the biggest change is the prevalence of literacy in the modern era. For the first time in history, even in third world countries and poor districts, most people can read.
All the information in the world is useless if you can't share it, and the amount of literate people, combined with recent technological developments, have made it possible to share the history of our human experience far beyond what we were capable of 100, 2000, even 50 years ago.
And in my experience, most people are willing to listen.
In case you don't get a ton of responses here, this would be a great question to post in a "theory Thursday" thread.
I would say the most obvious recent way in which the telling of history has changed is the rise of social history, which is related to the rise of postmodernism and focuses on telling the stories of common people who are often left out of the historical record. Social history is tied in with the rise of telling stories based around people's positions in the historical time period, and so it's related to the rise of things like queer history, gender history, black history, and the like. (Marxism has also contributed to this by giving us a framework to understand conflicts among groups, and even our understanding of race/gender, based on economic status and privilege.)
This is a very brief overview, of course.