I mean when did people start studying the past, simply to know about it rather than to repeat some tale that made them or their civilisation look great? Who was the first historian in various cultures and what specifically did they do that qualifies them as a real historian?
This is a really difficult question to answer. The history of the methods of studying history is known as 'Historiography'.
In Western Culture the Age of Enlightenment is generally seen as the cradle from which modern historical method sprung. In England Edward Gibbon is seen as one of the first people to practice history in the sense we now understand it.
I would argue that the the specific qualification that you ask for in the question is a dedication to studying and recording what actually happened through analysis of evidence rather than merely parroting folk tales etc.
In this sense some writers pre-enlightenment can be seen to have shown signs of practicing historical method. An English example would be that the medieval writer William of Newbrugh condemned his contemporary Geoffrey of Monmouth for inventing stories as history rather than recounting what actually happened. Therefore William shows some signs of a method of source analysis which is similar to the modern study of history.
For a good introduction into the history of history try wikipedia page for 'Historiography' as it cites many landmark historical works and their authors.