Elements on the periodic table are arranged based on how many protons and electrons each element has. Protons are positively charged and are found the in the nucleus along with neutrons. Electrons, which are much smaller than protons, are negatively charged and are found in orbitals ('shells') around the nucleus.

The families of elements are arranged in columns on the periodic table. Elements in the same family have similar properties because they have similar electron configurations. The atomic number (Z) of an element tells us how many protons (and electrons) an atom has. For example, magnesium (Mg, Z=12) has 12 protons and 12 electrons and calcium (Ca, Z=20) has 20 protons and 20 electrons. Even though Mg and Ca have different atomic numbers, they are in the same family because they both have the same electron configuration - full s-orbitals.

What does that mean? Atoms have s, p, d, and f-orbitals. Each s-orbital hold 2 electrons, p-orbtials hold 6, d-orbitals hold 10, and f-orbitals hold 14 electrons. They fill with electrons in the order:

1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f6d7p. Mg has 2 electrons in 1s, 2 electrons in 2s, 6 electrons in 2p, and 2 electrons in 3s, totaling 12 electrons. Only the outermost (valence) orbital matters in determining which family the element is in. Magnesium's outermost orbital is the filled 3s-orbital and calcium's outermost orbital is the filled 4s-orbital. All elements in that family have filled s-orbitals.

The columns of the periodic table are arranged by valence orbital. The first two columns are for the s-orbitals. Columns 3-12 are known as the d-block elements because their valence orbital is the d-orbital. Columns 13-18 are the p-block elements. Column 13 elements have one electron in their outermost p-orbital while column 18, the noble gases, have filled outermost p-orbitals. The two rows at the very bottom of the periodic table are the f-block elements.

Here is a really great periodic table from the National Institute of Standards that shows all of the electron configurations for all of the atoms