What is salvation? Salvation means to be saved, or rescued.  When we hear the word "salvation", it means that there is something we need to be saved from.  We need to be saved
from Hell.  What is Hell? Hell is being under God's "wrath".  The word "wrath" means anger.  Therefore, God is angry.

“For a fire is kindled in mine anger, and shall burn unto the lowest hell, and shall consume the earth with her increase, and set on fire the foundations
of the mountains." (Deuteronomy 32:22)
“God judgeth the righteous, and God is angry [with the wicked] every day." (Psalms 7:11)
“The wicked shall be turned into hell, [and] all the nations that forget God." (Psalms 9:17) 

Hell is spoken of as a lake of fire that will never be put out.

“But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death." (Revelation 21:8)
“And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never
shall be quenched: Where their worm dieth not, and the fire is not quenched." (Mark 9:43-44) 

We are all sinners and deserve to go to Hell.

“If we say that we have no sin, we deceive ourselves, and the truth is not in us." (1 John 1:8)
“For all have sinned, and come short of the glory of God;" (Romans 3:23) 

God must send us to Hell to make payment for sin.

“For the wages of sin [is] death; but the gift of God [is] eternal life through Jesus Christ our Lord." (Romans 6:23) 

We can't save ourselves from Hell just because we don't want to go there.  God doesn't save us from Hell according to our wish to be saved, but according
to His mercy.

"Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;" (Titus 3:5)
“For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. So then [it is] not of him that willeth, nor of him that runneth, but of God that sheweth mercy." (Romans 9:15-16) 

God has already chosen those He would save from Hell.

“According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love:" (Ephesians 1:4)
“For whom he did foreknow, he also did predestinate [to be] conformed to the image of his Son, that he might be the firstborn among many brethren." (Romans 8:29) 

God punished Jesus for the sins of the people He chose to save from Hell.  Jesus made the payment for sin that God's chosen people should have paid.

“Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed [is] every one that hangeth on a tree:" (Galatians 3:13)
“For he hath made him [to be] sin for us, who knew no sin; that we might be made the righteousness of God in him." (2 Corinthians 5:21) 

In order to be saved from Hell, we must be under the hearing of the Bible.

“So then faith [cometh] by hearing, and hearing by the word of God." (Romans 10:17) 

When God saves us, He gives us a new heart and spirit that has already been cleansed by the sacrifice of Jesus, and does away with our natural old spirit.

“A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh." (Ezekiel 36:26)
“Therefore if any man [be] in Christ, [he is] a new creature: old things are passed away; behold, all things are become new." (2 Corinthians 5:17) 

This is referred to as being born again. 

“Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God." (John 3:3)
“Marvel not that I said unto thee, Ye must be born again." (John 3:7)
“Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever." (1 Peter 1:23) 

When a person God has chosen is saved by God from Hell, God gives that person the Spirit of God.

“But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his." (Romans 8:9) 

Because Jesus is God, the Spirit of God is the Spirit of Jesus.  If we have the Spirit of Jesus, we have the son of God and eternal life.

“He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him." (John 3:36)
“He that hath the Son hath life; [and] he that hath not the Son of God hath not life." (1 John 5:12)