In a small way this question falls into the wonderful world of historiography, which mostly covers what history is actually made up of and how history is influenced by the author. However, in a small way, it also studies the history of history itself. The question is challenging, and history began being recorded differently and at different times throughout the world.

Most historians agree that the idea and outlook of recorded history, at least similarly to how we know it today, began in Mesopotamia. Often the Greek historian Herodotus is credited with being the first historian of Western History and lived and wrote during the fifth century BCE. His work was mostly focused on the origins of the Greco-Persian war and is credited with attempting to write history free of myth. "Attempting" is the key word there as his history is still wrought with legend and myth and a large amount of Greco bias, which would not pass for peer-reviewed history today. Yet Herodotus' study of past events from a political, social, and economic standpoint, serve as a basis for how history is studied today. In the same respect, the Hebrew Bible is also considered an early version of history, however, like Herodotus, cannot be considered the same type of history we know today.

I cannot speak to the founding fathers of other areas of history and maybe others can add to that realm.

Sources and further reading see: Herbert Butterfield's 1981 "The Origins of History" or for readings in Historiography, Barbara Tuchman's 1982 "Practicing History"

The oldest known cave art comes from the Cave of El Castillo in northern Spain. Hand stencils and disks made by blowing paint onto the wall in El Castillo cave were found to date back to at least 40,800 years, making them the oldest known cave art in Europe, 5–10,000 years older than previous examples from France.

So I guess we have been documenting history for at least 40,800 years.

However, the earliest known systematic historical thought emerged in ancient Greece, a development which would be an important influence on the writing of history elsewhere around the Mediterranean region. The earliest known critical historical works were The Histories, composed by Herodotus of Halicarnassus (484 – c. 425 BCE) who later became known as the "father of history".

The act of writing history, as you might imagine, has been going on for quite a long time. In the West, the modern, empirical approach to history, however, began in Germany in the 19th century, led by a man named Leopold von Ranke. Essentially, they began the trend of taking the past on its own terms, using primary sources, and the critical method of history.

Modern historical writing has also broken up into a myriad of different methodologies, lenses, and schools of thought. Well, maybe broken up isn't the best choice of words, but I think you catch my meaning. For instance, an economic history would focus on economic factors and how they influenced changes in society. Looking at history using a racial methodology would focus on how race as affected an event or social group. Methodologies are by no means always mutually exclusive, have great amounts of overlap, and are constantly evolving.

There is a thought that the first historical event recorded was at the site of Catal Hoyuk in the form of a volcanic eruption: http://s710.photobucket.com/user/volcanism2/media/volcano-art/catalhoyuk2.jpg.html