Why does God forgive? God forgives because each person has eternal value worth more than the whole world (Matthew 16:26) and He wants them to be saved. God so valued each person that he offered His only begotten Son as sacrifice.
How does God forgive? God forgives generously. One of the greatest statements in the Bible concerning God’s forgiveness occurs in Psalm 103:10-14. "He hath not dealt with us after our sins; nor rewarded us according to our iniquities. For as the heaven is high above the earth, so great is his mercy toward them that fear him. As far as the east is from the west, so far hath he removed our transgressions from us. Like as a father pitieth his children, so the LORD pitieth them that fear him. For he knoweth our frame; he remembereth that we are dust."
Who does God forgive? God forgives all men potentially and the penitent actually. As indicated by the future tense, Jesus spoke about potential forgiveness in Mark 3:28 “All sins shall be forgiven unto the sons of men, and blasphemies wherewith soever they shall blaspheme.” Actual forgiveness, however, comes when an individual repents and turns to God in obedience (Mark 4:12).
The perfect standard for behavior is God, and the gospel exhorts all to be perfect as God is perfect. This entails that one imitate God as much as is possible. “Be ye therefore imitators of God, as beloved children” (Ephesians 5:1 ASV). We would do well to imitate God when it comes to forgiveness. Second Peter 3:9 says that God “not willing that any should perish but that all should come to repentance.”