How does God draw people to Jesus?

Notice the attitude that characterizes a Christian. It is one of total devotion and motivation despite of any loss to gain Christ. It is a singular focus and desire to be found in Him no matter the cost.

This compelling and obsession that marks a Christian is because of the weight and gravity of the love of God to have you as His own, in spite of your sinful works against Him.

John 6:44  No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day.
Romans 1:16  For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek.
 
Hosea 11:4  I led them with cords of kindness, with the bands of love, and I became to them as one who eases the yoke on their jaws, and I bent down to them and fed them.
 
Jeremiah 31:3  the LORD appeared to him from far away. I have loved you with an everlasting love; therefore I have continued my faithfulness to you.
 
John 6:68  Simon Peter answered him, "Lord, to whom shall we go? You have the words of eternal life,
 
Luke 14:23  And the master said to the servant, 'Go out to the highways and hedges and compel people to come in, that my house may be filled.
 
Luke 14:26  "If anyone comes to me and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be my disciple.
 
Acts 3:25-26  You are the sons of the prophets and of the covenant that God made with your fathers, saying to Abraham, 'And in your offspring shall all the families of the earth be blessed.'  (26)  God, having raised up his servant, sent him to you first, to bless you by turning every one of you from your wickedness."
 
1 Corinthians 1:24  but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God.
 
Philippians 3:8-21  Indeed, I count everything as loss because of the surpassing worth of knowing Christ Jesus my Lord. For his sake I have suffered the loss of all things and count them as rubbish, in order that I may gain Christ  (9)  and be found in him, not having a righteousness of my own that comes from the law, but that which comes through faith in Christ, the righteousness from God that depends on faith-- (10)  that I may know him and the power of his resurrection, and may share his sufferings, becoming like him in his death,  (11)  that by any means possible I may attain the resurrection from the dead.  (12)  Not that I have already obtained this or am already perfect, but I press on to make it my own, because Christ Jesus has made me his own.  (13)  Brothers, I do not consider that I have made it my own. But one thing I do: forgetting what lies behind and straining forward to what lies ahead,  (14)  I press on toward the goal for the prize of the upward call of God in Christ Jesus.  (15)  Let those of us who are mature think this way, and if in anything you think otherwise, God will reveal that also to you.  (16)  Only let us hold true to what we have attained.  (17)  Brothers, join in imitating me, and keep your eyes on those who walk according to the example you have in us.  (18)  For many, of whom I have often told you and now tell you even with tears, walk as enemies of the cross of Christ.  (19)  Their end is destruction, their god is their belly, and they glory in their shame, with minds set on earthly things.  (20)  But our citizenship is in heaven, and from it we await a Savior, the Lord Jesus Christ,  (21)  who will transform our lowly body to be like his glorious body, by the power that enables him even to subject all things to himself.
 
Psalms 110:3  Your people will offer themselves freely on the day of your power, in holy garments; from the womb of the morning, the dew of your youth will be yours.
 
When you consider your own conversion, always remember to ask yourself the question, “Why did I come, why did I see the great need for a Savior?” The answer is clear. God Himself, by His love, mercy, and grace, compelled you by the Holy Spirit and the Power of His Word to rescue you from your sin. He sovereignly gave you a new heart that would be able to respond to the Gospel call and be saved.
 
Philippians 2:13  for it is God who works in you, both to will and to work for his good pleasure.