How did Archbishop James Ussher calculate that the world was created 6000 years ago?
Ussher calculated the date of the creation of the world by working his way back through the narrative given in the Bible. Given his presuppositions, he was a careful and thorough scholar, and modern critics of creationism such as Stephen Jay Gould have defended his academic respectability, while rejecting the conclusions he came to.
Following the Bible was not as simple as it sounds. For one thing, there are variant texts for the early period from Adam to Solomon. Ussher here followed the readings of the Hebrew Bible, which resulted in a count about 1500 years shorter than the ages given in the Septuagint would have yielded. For the time after Solomon, the Biblical record becomes more difficult to work with, and Ussher had to rely on external datings of events and figures mentioned in the sacred text. With the limitations of historical and archeological knowledge in his time, this was obviously tricky and difficult work.
For the precise date and time of the creation, Ussher calculated from the Jewish calendar, the seven-day length of the process as given in Genesis, and contemporary astronomical tables. He thus arrived at the conclusion that the world had been created at "the entrance of the night preceding the twenty third day of Octob[er] in the .... year before Christ 4004."