John Dalton arranged the elements in order of atomic weights which he measured by doing some chemical reactions. He published his table of elements a few months later
John Newlands also arranged the elements in atomic weight but he observed the table closly and saw that every 8th element seem similar properties. A produced a table called the law of octaves however he was very stubborn and made the table even tho new elements were being discovered so he still filled in his octaves even though some were not similar at all
A russian chemist named Dmitri mandeleev made the breakthrough. He placed them in the order of atomic mass and he arranged them so that a periodic pattern in their properties could be seen. He left gaps for elements that were not discovered and predicted their properties and overtime people discovered these elements and he was a hero in the eyes of all the chemists around the world.