God is saving men today by imputing to them the righteousness of Christ when they believe the gospel for today.

Imputation is the charging of something to someone's account.

Righteousness is purity of heart, and includes all we call justice, honesty and virtue. 

Righteousness is required in order to be with God:

Psalm 34:15 (KJV) The eyes of the LORD are upon the righteous, and his ears are open unto their cry.

Proverbs 15:29 (KJV) The LORD is far from the wicked: but he heareth the prayer of the righteous.

Matthew 5:20 (KJV) For I say unto you, That except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven.

Romans 6:22 (KJV) But now being made free from sin, and become servants to God, ye have your fruit unto holiness, and the end everlasting life.

The imputation of Christ's righteousness to men is necessary because men have no righteousness of their own

Scripture tells us that there are no righteous men:

Romans 3:10 (KJV) As it is written, There is none righteous, no, not one:

Even a man's best efforts at being righteous fall short before God:

Isaiah 64:6a (KJV) But we are all as an unclean thing, and all our righteousnesses are as filthy rags;

Christ on the other hand is righteous... 

1 John 2:1b (KJV)​ Jesus Christ the righteous:

... and Christ can be a man's righteousness:

 Corinthians 1:30 (KJV) But of him are ye in Christ Jesus, who of God is made unto us wisdom, and righteousness, and sanctification, and redemption:

Becoming righteous in God’s eyes

When a man believes the gospel of grace, God counts this belief for righteousness and credits this righteousness to the man’s account:

Romans 4:3, 23-24 (KJV) For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness...23 Now it was not written for his sake alone, that it was imputed to him; 24 But for us also, to whom it shall be imputed, if we believe on him that raised up Jesus our Lord from the dead;

This is possible because the gospel of grace…

1 Corinthians 15:3-4 (KJV) For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures:

…contains the elements which enable a man to be made right (justified) before God:

Romans 4:25 (KJV) Who [speaking of Christ] was delivered for our offences, and was raised again for our justification.

The principle and application of imputation is seen under the old testament, where each year on the Day of Atonement Israel’s sins were transferred (imputed) to an innocent goat and the innocence of the goat was transferred (imputed) to Israel:

Leviticus 16:21-22 (KJV) And Aaron shall lay both his hands upon the head of the live goat, and confess over him all the iniquities of the children of Israel, and all their transgressions in all their sins, putting them upon the head of the goat, and shall send him away by the hand of a fit man into the wilderness: 22 And the goat shall bear upon him all their iniquities unto a land not inhabited: and he shall let go the goat in the wilderness.

 In summary, God saves men today by imputing (transferring, crediting) to men the righteousness of Christ when they believe the gospel which tells of his atoning work in his death, burial and resurrection.

See also Imputed Righteousness