How were the elements arranged in Dmitri Mendeleev's periodic table?
Through each element's property.
Each element has its own unique property. What Mendeleev did was experiment and record many different properties of each element, classifying each with other elements of similar properties. At the time, there was only a handful of elements; not as much as today.
For example, Noble Gases were discovered to be non-reactive, so they were grouped together, while Akali metals were found to be extremely reactive, thus they were grouped together.
Not sure if he did that, but same concept.
I would include Mendeleev's works here, but it's in Russian and I can't read it ¯l_(ツ)_l¯