How do the periodic table trends occur chemically?

[Anthony]

So on looking at a periodic table, why do the trends below appear, based on their nuclear charge and electron shielding? I know how the trend goes (e.g. Atomic size generally increases down a group to the left), but why does the trend occur? Also note any deviance from those trends.

Atomic Size
Ionization Energy
Electron Affinity
pH
Metallic behavior
Ion size (not the same as atomic size)