The periodic table organizes the elements according to increasing atomic number. Early scientists like Dobereiner, Newlands, and Mendeleev made attempts to classify elements, with Mendeleev devising the first successful periodic table. Mendeleev arranged elements with similar properties into columns and left gaps for elements not yet discovered. The periodic table provides information on elemental properties like valency, atomic size, metallic character, and electronegativity based on an element's position.