Does man have free will to be a believer in God? How can man be saved? Can man accept God and be a believer or does God have to approach man?
Man certainly has free will. Otherwise God would be unjust to choose some to be saved and others to be lost based just on his whim. The problem with those who say that once a person is saved he cannot lose his salvation is that such a doctrine necessarily requires the belief that man does not have free will. I have addressed that part of the question at What Does the Bible Say About..Once Saved, Always Saved?
Logically, one could argue that it makes no sense for God to give commandments to men if they have no choice in following them or not. One could not sin, because sin implies a choice to obey. If one has no choice but to violate a command, then logic says they can not be held accountable for the sin. But that is logic, not scripture. Fortunately, the scriptures also say man has free will.
“I call heaven and earth to record this day against you, that I have set before you life and death, blessing and cursing: therefore choose life, that both thou and thy seed may live.” (Deuteronomy 30:19)
“And if it seem evil unto you to serve the LORD, choose you this day whom ye will serve; whether the gods which your fathers served that were on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the LORD.” (Joshua 24:15)
“Envy thou not the oppressor, and choose none of his ways.” (Proverbs 3:31)
“Therefore to him that knoweth to do good, and doeth it not, to him it is sin.” (James 4:17) (If we had no choice, then knowing to do good would necessarily result in doing good.)
There are other passages as well, but these should suffice to show that man can make choices. The idea proposed by John Calvin that one is either destined for salvation or condemnation and must follow that course (“irresistible grace”) without the possibility of change just doesn’t take these scriptures into account.
I have never figured out why Presbyterians and many Baptists try to teach people about the gospel. If they believe that those God has chosen for salvation will necessarily come to obey the gospel, they don’t need to preach to them; God will see that they learn the truth some other way. If they believe that those God has chosen for condemnation can not do good, then it is a waste of time to teach them because they could never obey.
For how man can be saved, see my answer at What Does the Bible Say About..Salvation?
God has approached man by offering a savior for sin. Now it is up to man to accept that offering. We must approach God in the way that he has designated, in response to his approaching us. It’s a mutual thing, except God came the farthest in his approach to man.