The original periodic table was made by Dmitri Mendeleev, placing all known elements at the time in order and grouping elements by some of their common trends, even predicting some elements that they did not know about at the time.
The modern Periodic Table instead has elements grouped in rows and columns based on their properties. The elements are listed left to right in increasing atomic number, getting larger as you go down a column. Each row is known as a period and each column is known as a group.
The name of each group can be seen at the top of the Periodic table. For example, group 1A has Hydrogen, Lithium, Sodium, Potassium, Rubidium, Cesium, and Francium within it. All group B elements are known as transition metals, while all the group A elements are the main group elements. Some of the groups also have special names:
Everything on the periodic table to the left of the metalloids are metals. Metals are shiny, malleable, ductile, and good conductors of heat and electricity. To the right of the metalloids are nonmetals. Nonmetals are brittle, insulating, poor conductors, and dull. Metalloids have properties of both metals and nonmetals, some of which can even swap these properties around based on their condition!
The periodic table is organized in such a strange way for a few reasons. The first one we've already talked about, how it goes in increasing atomic number order. The next major reason for it is based on the properties of each element; all elements in a single column act similarly to one another. This is due to the patterns their orbitals make, how much they want to gain or lose electrons, and how tightly bound their electrons are. Two other strange things of note on the organization are that the table itself should be a spiral (since it's actually a continuous pattern) and that the groups at the bottom are actually in the table up above, they're just moved there to save space. If we were to make the periodic table with the lanthanides and actinides in the right location it'd look like this:
The periodic table can also be used to determine certain periodic trends, properties that can be determined based on an element's location on the periodic table. They are as follows:
Atomic Mass- The average amount of protons and neutrons in an atom.
Metallic Character- How reactive an element is as a metal.
Nonmetallic Character- How reactive an element is as a nonmetal.
Atomic Radius- The radius of the overall atom (including the electron cloud).
Electron Affinity- The likelihood of an electron to be gained by an element.
Ionization Energy- The energy required to remove an electron from the element.