The first records of an organized was sometime around 1870s. Dimitri Mendeleev and Lothar Meyer working independently developed the first ideas of a geometric presentation of the elements that organized them according to physical and chemical properties. It seems that over time, Mendeleev's tool held sway and has been continued to be developed over the last 140 years.
Mendeleev organized his table in order of increasing atomic mass and then grouped them together according to similar chemical and physical properties. Doing so he noted that there were gaps in the table where he predicted other to date unknown elements would one day be discovered. Subsequent forms of the Periodic Table have been ordered based on atomic number (that is, the number of protons in an element's nucleus) and arranged such that columns of elements have similar chemical and physical properties.
As was predicted, every naturally occuring element with atomic numbers of 1 through 92 have been discovered along with an additional 116 man-made elements.