Definition of Exegesis
Here's a description of what exegesis is from pages 21-22 of Roy B. Zuck's book titled Basic Bible Interpretation.
"The exegetical process takes place in the workshop, the warehouse. It is a process in private, a perspiring task in which the Bible student examines the backgrounds, meanings, and forms of words; studies the structure and parts of sentences; seeks to ascertain the original textual reading (textual criticism) etc. ... In the privacy of his study, the exegete seeks to comprehend the exact meaning of the Bible passing being studied."
Exegesis is the process of approaching Bible interpretation with a humble spirit, and an open mind. In order to gain a true understanding of God's Word, one must be willing to allow God's Word to speak for itself, and be willing to abandon cherished beliefs if they are in conflict with God's Word.
Exegesis is not merely an intellectual exercise we do all alone. God tells us that in order to properly understand His Word, we need the help of a) the Holy Spirit and b) others who have strong theological training. We are also cautioned to be careful about who we allow to influence us.
On needing the counsel of others:
Where no counsel [is], the people fall but in the multitude of counsellors [there is] safety.
On being careful about who you allow to teach you:ears; And they shall turn away [their] ears from the truth, and shall be turned unto fables.
Preach the word; be instant in season, out of season; reprove, rebuke, exhort with all longsuffering and doctrine. For the time will come when they will not endure sound doctrine; but after their own lusts shall they heap to themselves teachers, having itching
2 Timothy 42-4
It is vital that we approach Bible interpretation with humility. Much of God's truth and wisdom are in sharp contrast with today's political correctness and tolerance movements, and with modern secular psychology. When practicing true exegesis, be prepared to be viewed as foolish by an ignorant world that has placed its confidence in fallible human knowledge instead of the infallible knowledge of our all-knowing God and Creator.For the wisdom of this world is foolishness with God. For it is written, He taketh the wise in their own craftiness. And again, The Lord knoweth the thoughts of the wise, that they are vain. Therefore let no man glory in men. For all things are yours;
Let no man deceive himself. If any man among you seemeth to be wise in this world, let him become a fool, that he may be wise.
1 Corinthians 318-21
See also: Definition of "Exegesis" (Answers in Genesis link)