The Need for Salvation
The need for salvation is based on two issues — man’s condition and God’s character.

Man’s condition: all men are sinners. Romans 3:23 tells us that “all have sinned and fall short of the glory of God.” The penalty for sin is separation from God, making the unbeliever spiritually dead. Romans 6:23 states, “For the wages of sin is death.” The apostle Paul tells the Ephesians that they were “dead in their trespasses and sins” (Ephesians 2:1).

God’s character: God is holy and must separate Himself from sin (Psalm 97:2). God’s perfect justice demands that sin must be punished (Romans 6:23). All who present themselves before God must be holy without sin and have the righteousness of God (Revelation 21:8,27)

God’s Answer to Man’s Need
Motivated by His love for us, God solved the sin problem. He sent His only Son, Jesus Christ, to be our substitute (John 3:16; 1 John 2:2; 4:10). When Jesus Christ died on the cross, He paid the penalty for our sins, past, present, and future, and God’s justice was satisfied (Romans 3:21-26).

Salvation is by grace through faith (Ephesians 2:8). Man contributes nothing to nor does anything to deserve salvation. Man is saved by believing the simple gospel message: “… that Christ died for our sins, according to scriptures; And that he was buried, and that he rose again the third day according to the scriptures; And that he was seen…” (1 Corinthians 15:3-5).

The Response
What is the response? The Gospel of John is the only book written so that unbelievers would believe (John 20:30-31). John uses the word “believe” 85 times. The call to the world is to believe in Jesus, but in recent years the understanding of what it means to believe in Jesus has become cloudy.
To believe in Jesus is to understand and be convinced that,
1. Jesus is God who came in the flesh (John 1:1-14).
2. Jesus died for our sins on the cross, was buried, and rose again the third day. He paid the penalty for our sin with his death and sacrifice (1 Corinthians 15:3-5).
3. Jesus is the life-giver who gives freely eternal life as a gift (see below).

In other words, to believe in Jesus is to be convinced in who He is, in what He did, and that His promise is true. The one who believes, God’s righteousness is placed to that one’s account and the gift of eternal life is provided at the moment of belief.
Some have stated that belief includes being sorry for sin, making amends, turning over a new leaf, baptism, taking sacraments, leading a good life, or making allegiance to Jesus as Lord and King. While most of these ideas are advantageous, they are not required for eternal life and when added to the necessary response to the Gospel, it adds works and in effect tells Jesus that you do not believe that eternal life is a free gift.

Verses
Genesis 15:6 - Then he believed in the Lord, and He reckoned it to him as righteousness

Psalm 32:1-2 - How blessed is he whose transgression is forgiven, Whose sin is covered! How blessed is the man to whom the Lord does not impute iniquity, And in whose spirit there is no deceit!

John 3:17-18 - "For God did not send the Son into the world to judge the world, but that the world might be saved through Him. "He who believes in Him is not judged; he who does not believe has been judged already, because he has not believed in the name of the only begotten Son of God.

John 5:24 - Truly, truly, I say to you, he who hears My word, and believes Him who sent Me, has eternal life, and does not come into judgment, but has passed out of death into life.

John 6:28-29 - Therefore they said to Him, "What shall we do, so that we may work the works of God?" Jesus answered and said to them, "This is the work of God, that you believe in Him whom He has sent."

John 10:28-30 - ...and I give eternal life to them, and they will never perish, and no one will snatch them out of My hand. "My Father, who has given them to Me, is greater than all; and no one is able to snatch them out of the Father's hand. I and the Father are one.

John 11:25-26 - Jesus said to her, "I am the resurrection and the life; he who believes in Me will live even if he dies,  and everyone who lives and believes in Me will never die. Do you believe this?"

John 20:30-31 - Therefore many other signs Jesus also performed in the presence of the disciples, which are not written in this book; but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name.

Romans 3:20, 22-24, 28 - because by the works of the Law no flesh will be justified in His sight; for through the Law comes the knowledge of sin. ... even the righteousness of God through faith in Jesus Christ for all those who believe; for there is no distinction; for all have sinned and fall short of the glory of God, being justified as a gift by His grace through the redemption which is in Christ Jesus; ... For we maintain that a man is justified by faith apart from works of the Law.

Romans 4:4-5 - Now to the one who works, his wage is not credited as a favor, but as what is due. But to the one who does not work, but believes in Him who justifies the ungodly, his faith is credited as righteousness,

Romans 6:23 - For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord.

Galatians 2:16 - Nevertheless knowing that a man is not justified by the works of the Law but through faith in Christ Jesus, even we have believed in Christ Jesus, so that we may be justified by faith in Christ and not by the works of the Law; since by the works of the Law no flesh will be justified.

Ephesians 2:4-5, 8-9 - But God, being rich in mercy, because of His great love with which He loved us, even when we were dead in our transgressions, made us alive together with Christ (by grace you have been saved), ... For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, so that no one may boast.

Philippians 3:9 - And may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith,

Titus 3:5 - He saved us, not on the basis of deeds which we have done in righteousness, but according to His mercy, by the washing of regeneration and renewing by the Holy Spirit,

1 John 5:13 - These things I have written to you who believe in the name of the Son of God, so that you may know that you have eternal life.