How should a Christian deal with feelings of guilt regarding past sins?

TL;DR:

Jesus didn’t forgive your sins halfway—He removed them completely. Because of this, we should live in the grace of our redemption, not the guilt of our past sins.

The Bible tells us that all people have sinned (Psalm 51:5; Romans 3:23). Even once we are saved, sin will still be a part of our lives, as it was for the apostle Paul (Romans 7:14-25). This sin, however, no longer defines who we are if we are saved by belief in Christ (2 Corinthians 5:17). Salvation through Christ blots out our mistakes, no matter how minor or heinous they may be. Forgiveness from God, through Christ, is available to all and is sufficient for covering every wrong we have committed (Psalm 32:5, 85:2, 86:5; Romans 6:23; 1 Corinthians 6:9-11; 1 John 1:9). The Bible tells us that God has removed our sins "as far as the east is from the west" (Psalm 103:12). Jesus' interaction with Zacchaeus is a great example of this in Luke's gospel.

The Bible also reminds us that our enemy, the devil, is known as the accuser and he constantly tries to remind us of our past failures (Revelation 12:10). Jesus called Satan "The Father of Lies"; the Devil and will do everything he can to make us believe his lies, including that our past sins are unforgiven or still define us. The truth of Scripture reminds us that we have grace from God for every shortcoming and identity in His salvation, not in our sin.

from the old testament

All human beings are born with sin. David wrote, "Surely I was sinful at birth, sinful from the time my mother conceived me (Psalm 51:5). Believers should realize that whatever sins they committed in the past are sins that many other people have also committed, but God grants repentent sinners forgiveness.
David found joy and restoration in God's forgiveness: "Then I acknowledged my sin to you [God] and did not cover up my iniquity . . .And you forgave the guilt of my sin" (Psalm 32:5)
God forgives all sin, not just some, and shows His goodness and love for us through His forgiveness (Psalm 85:2, 86:5). He removes our transgressions "as the east is from the west" (Psalm 103:12).

from the new testament

Sin is part of the human condition. Paul wrote, "For all have sinned and fall short of the glory of God" (Romans 3:23).
But we can be redeemed through Christ. Zacchaeus' interaction with Jesus illustrates that anyone can be restored when they encounter Jesus and repent. Zacchaeus made amends to those who he had sinned against (Luke 19:8), and we can do the same.
After Paul describes his struggle with sin in Romans 7, he writes in Romans 8:1, "Therefore, there is now no condemnation for those who are in Christ Jesus." Continued guilt over past sins means we are keeping ourselves in chains when Christ has already freed us. God can erase any sin (1 Corinthians 6:9-11)
We must confess them, though. Some who may be bothered by past sins may not have confessed them to God. The apostle John indicates that God is ready to forgive when we confess our sins to Him: "If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness" (1 John 1:9, 2:1).
Paul describes the aftermath of coming to salvation in Christ as becoming a "new creation" (2 Corinthians 5:17). Though we still may sin, we don't lead a lifestyle of sin nor do we love sin.
Failure to accept the forgiveness that Christ provides is one of the Devil's tactics to discourage believers. Revelation calls the Devil "the accuser of our brothers and sisters" (12:10).

implications for today

Some monastic orders in the past have existed on a bland diet of bread and water, fasted for days on end, take vows of silence and celibacy, and worn uncomfortable clothes (hair shirts, anyone?). Christians today who wallow in their past sins may not go as far, but they are punishing themselves for sins that Christ has already forgiven them of.

But nearly every believer will come to a point, especially if they're newly Christian, in which they'll look back on their life before Christ and identify sins that they didn't even treat as sins at the time.

Sometimes unconfessed sin is the root of that guilt. In that case, we can confess our sins to God and know He will forgive us (1 John 1:9).

If our sins were committed to others, we may need to apologize to them and, if possible, rectify the relationship. Even if they do not choose to forgive us or allow the relationship to heal, we can know that we have done our part to deal with our sinful behavior.

If guilt remains after these steps, most likely lies from the enemy are causing it. We can ask God to help us stand against the attacks of the deceiver and to believe His truth.

understand

Everyone has sinned and missed the perfection God requires.
God promises forgiveness and cleansing for any past sin that we have repented of.
Guilt over past sin can be legitimate regret or an untrue accusation from the enemy.

reflect

How does guilt or shame over past sins impact your life now?
How does knowing the Devil is an accuser and liar affect your view of your guilt over past sin?
How do your feelings of guilt and shame change when you remind yourself of the truth that God has forgiven your sins when you trusted in Him for salvation?

engage

How can we remind ourselves that God has forgiven past sins we have repented of?
Why might it be important to make amends with people we have sinned against in order to overcome feelings of guilt?
How can we identify ways that the enemy is lying to us about the state of past sin in our lives, and what truth should we hold onto instead?