Prevenient grace is the grace that precedes.
A Calvinist believes in prevenient grace as the grace that precedes salvation. An article on the question #50 on monergism.com states, "It is true, of course, that the regenerating grace of God must come before faith, and so in that sense it is prevenient." It is believed by Calvinists that "God grants his quickening grace to unbelievers, it does not merely given them the option to be alive--it makes them alive." In other words only the elect receive this grace but the nonelect only receive hell in its fullest without any chance for salvation (for God's glory, of course).
J. I. Packer in an article on "Regeneration" from his theology book "Concise Theology" writes,
"Regeneration is monergistic: that is, entirely the work of God the Holy Spirit. It raises the elect among the spiritually dead to new life in Christ (Eph. 2:1-10). Regeneration is a transition from spiritual death to spiritual life, and conscious, intentional, active faith in Christ is its immediate fruit, not its immediate cause. Regeneration is the work of what Augustine called 'prevenient' grace, the grace that precedes our outgoings of heart toward God."
A classical/reformed Arminian or Wesley Arminian would believe that since all humanity is dead because of sin, no one seeks God. NO ONE SEEKS GOD! So the Scripture teaches in Romans 3:9-18. God is the first. God initiates. God seeks mankind. No human seeks God. God is the one who begins and ends salvation. Every single human being would absolutely go to hell deservingly so unless God starts, initiates, begins, and seeks mankind.
A. W. Tozer wrote,
"Christian theology teaches the doctrine of prevenient grace, which briefly stated means this, that before a man can seek God, God must first have sought the man.
Before a sinful man can think a right thought of God, there must have been a work of enlightenment done within him; imperfect it may be, but a true work nonetheless, and the secret cause of all desiring and seeking and praying which may follow.
We pursue God because, and only because, He has first put an urge within us that spurs us to the pursuit. "No man can come to me," said our Lord, "except the Father which hath sent me draw him," and it is by this very prevenient drawing that God takes from us every vestige of credit for the act of coming. The impulse to pursue God originates with God, but the outworking of that impulse is our following hard after Him; and all the time we are pursuing Him we are already in His hand: "Thy right hand upholdeth me."
In this divine "upholding" and human "following" there is no contradiction. All is of God, for as von Hegel teaches, God is always previous. In practice, however, (that is, where God's previous working meets man's present response) man must pursue God. On our part there must be positive reciprocation if this secret drawing of God is to eventuate in identifiable experience of the Divine. In the warm language of personal feeling this is stated in the Forty-second Psalm: "As the hart panteth after the water brooks, so panteth my soul after thee, O God. My soul thirsteth for God, for the living God: when shall I come and appear before God?" This is deep calling unto deep, and the longing heart will understand it.
–Excerpted from A. W. Tozer, The Pursuit of God, chapter 1 (this was found on evangelicalarminians org.
Thus God gets all the glory for salvation. When Jesus commanded, "Repent" a person can resist or not resist. "You stiff-necked and uncircumcised in heart and ears! You always resist the Holy Spirit; as your fathers did, you also do. (Acts 7:51, EMTV)
Most Calvinists and Arminians preach the Gospel. Starting with the Law of God showing all that they are not good but evil and are deserving of hell fire, they proceed to the grace of God found only in the shed blood of Jesus Christ, who is the only savior.
But the Scripture has confined all under sin that the promise by faith in Jesus Christ might be given to those who believe. (Galatians 3:22, NKJV)