How many elements were listed on the first Periodic Table of the Elements?

In 1789, Antoine Lavoisier published a list of 33 chemical elements, grouping them into gases, metals, nonmetals, and earths; Chemists spent the fnext one hundred years searching for a more accurate classification scheme.
In 1829, Johann Wolfgang Dobereiner observed that many of the elements could be grouped into "triads" based on their chemical properties. (Eg. Lithium, sodium, and potassium, were grouped together in a triad as soft, reactive metals).

Russian chemistry professor Dmitri Mendeleev and German chemist Julius Lothar Meyer independently published their periodic tables in 1869 and 1870, respectively.
Mendeleev's table was his first published version; that of Meyer was an expanded version of his (Meyer's) table of 1864.] They both constructed their tables by listing the elements in rows or columns in order of atomic weight and starting a new row or column when the characteristics of the elements began to repeat.

The recognition given to Mendeleev's table came from two decisions he made.
1.He left gaps gaps in the table when it seemed that the corresponding element had not yet been discovered. (Mendeleev was not the first chemist to do this, but he was the first to be recognized as using the trends in his periodic table to predict the properties missing elements),
2. He ignored the order suggested by the atomic weights and switch adjacent elements, such as tellurium and iodine, to better classify them into chemical families.

https://en.wikipedia.org/wiki/Periodic_table#First_systemization_attempts

There were 60 known elements in 1860 when Mendeleev published his Periodic Table.

The Periodic Table of Elements

CIENTISTS HAD IDENTIFIED over 60 elements by Mendeleev's time. (Today over 110 elements are known.) In Mendeleev's day the atom was considered the most basic particle of matter. The building blocks of atoms (electrons, protons, and neutrons) were discovered only later. What Mendeleev and chemists of his time could determine, however, was the atomic weight of each element: how heavy its atoms were in comparison to an atom of hydrogen, the lightest element.
"I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and this soon convinced me that the properties of elements are in periodic dependence upon their atomic weights."
--Mendeleev, Principles of Chemistry, 1905, Vol. II

http://www.aip.org/history/curie/periodic.htm

Russian chemist Dmitri Mendeleev .. although he is often regarded as the father of the Periodic Table, Mendeleev himself called his table, or matrix, the Periodic System. Other people, like Londoner John Newlands, Frenchman Alexandre Béguyer de Chancourtois and German Julius Lothar Meyer made important contributions to the first Periodic Table but the main credit goes to Mendeleev. All of them were helped by the publication in 1860 of more accurate atomic weights, as relative atomic masses were then called. There were two main problems about establishing a pattern for the elements. First only 60 elements had been discovered (we now know of over 100) and second some of the information about the 60 was wrong. It was if Mendeleev was doing a jigsaw with one third of the pieces missing, and other pieces bent!

Mendeleev had written the properties of elements on pieces of card and tradition has it that after organising the cards while playing patience he suddenly realised that by arranging the element cards in order of increasing atomic weight that certain types of element regularly occurred. For example a reactive non-metal was directly followed by a very reactive light metal, then a less reactive light metal. The image of a stamp collectors' miniature sheet shows a stamp commemorating the hundredth anniversary of the Periodic Table superimposed on some of Mendeleev published the Periodic System. Shortly after, his ideas were presented to the Russian Physico-chemical Society. They were read by Professor Menschutkin because Mendeleev was ill. His ideas were then published in the main German chemistry periodical of the time, Zeitschrift f?r Chemie.

http://www.rsc.org/Education/Teachers/Resources/periodictable/pre16/develop/mendeleev.htm