How do the valency and the atomic size of the elements vary while going from left to right along a period in the modern periodic table ?

On moving from left to right in the periodic table valency increases up to 4 and then decreases.

The electrons present in the last shell determine the valency of a particular element. 

If the number of valence electrons is less than or equal to 4, valency= number of valence electrons If the number of valence electrons is more than 4, valency = 8 - a number of valence electrons. 

Atomic size decreases along a period. This is because on moving across a period, the number of valence shells remains the same and the electrons increase by one unit. As a result, the nuclear charge increases and thus, the atomic radius decreases.