Proverbs 26:1-12 gives advice on how to behave when dealing with fools. But who is a fool?
Some of the characteristics and definition of a fool according to the Bible are:
A fool says in his heart, “There is no God”, They are corrupt and they do abominable deeds (Psalm 14:1)
A fool has no delight in in understanding, but only in expressing his own opinion (Proverbs 18:2)
A fool has no self-control with his tongue but utters all his mind bringing ruin to himself (Proverbs 29:11; Proverbs 18:7)
A fool despises wisdom and instruction (Proverbs 1:7)
A fool is like one who builds his house upon the sand, because he/she hear the words of Jesus but does nothing about it (Matthew 7:26)

So with an understanding of who a fool is, how are we as followers of Christ Jesus, to deal with them?

When dealing with fools, we must not answer nor heed the arguments of a fool, lest we also become like him. On the other hand,  when it is determined, that a fool’s position must  be challenged, it is important to answer the fool according to his own folly, lest he is wise in his own eyes. In other words, we must know when to heed and when not to heed to a fool.

Proverbs 26:4-5 (KJV)
4
Answer not a fool according to his folly, lest thou also be like unto him.
5 Answer a fool according to his folly, lest he be wise in his own conceit.