John Dalton is best known for his work on development of atomic theory. He was a popular Chemist, meteorologist and Physicist of his times.
The period table is basically a tabular form of displaying chemical elements. The current form of the periodic table is a result of decades of experimentation and hard work of various chemists.
Dmitri Mendeleev is normally credited with the invention of Periodic Table. John Dalton did not arrange the periodic table. However, he brought in his atomic theory which had five postulates that are still valid. With this development, it became clear that Mendeleev has arranged the periodic table in order of increasing atomic number.
This helped the chemists in discovery of new elements.