How does atomic size vary on the periodic table?

Atomic size decreases across a Period from left to right as we face the Table, but INCREASES down a Group, a column of the Periodic Table. This is one of the most fundamental and useful ideas you can learn as you are introduced to chemistry.

Consider the diagram,

Atomic size is influenced by (i) nuclear charge, #Z#, and by (ii) shielding by other electrons. Incomplete electronic shells shield nuclear charge VERY ineffectively. The result? As we add electrons to the same valence shell, we also add protons to the nuclear charge. And thus across the Period #"nucular charge"# predominates, and draws the valence electrons towards the nuclear core, with the result of a marked decrease in atomic radius. Is this evident in the diagram?

Once a valence shell is filled, the nuclear charge is shielded with reasonable effect. A new quantum shell is initiated, farther from the nuclear core, with the Periodic pattern again repeated across the new Period.

I urge you to read your text in this respect. This contest between nuclear charge, #Z#, and shielding by other electrons, underlies the pattern of the Periodic Table, and the electronic structure of course determines the reactivity of each element. Capisce?