While the sin offering atoned for sins against God, the guilt offering (traditionally called the "trespass offering") was for sins against others. It also included making restitution which meant paying damages with interest (20%). The offerer had to confess his sin to God and a ram was offered. Only then could he receive forgiveness. It was similar to the sin offering in that it was mandatory. The major difference was that the sin offering was used when there could be no restitution.
Leviticus 6:8-30 involves specific procedures the priests were to follow for the burnt, grain, and sin offerings.
I once had a pair of really expensive sewing scissors that my mom entrusted to me while I was away at college. During one of the many activities during Rush Week in my sorority (I know, you are astonished that I was in a sorority, but it is true), my scissors were borrowed, but they were never returned. Someone lost them, but no one knew who. I had entrusted them to someone, and she loaned them out to the next girl, who loaned them out to the next girl, and so on. When I went to retrieve my scissors, everyone was very sorry that my scissors were gone, but since each person did not think they were the particular person who lost them, no one saw any need to replace them. I had many apologies but no restitution. This situation reminded me of the purpose of the guilt offering: Restitution.
The Holman Old Testament Bible Commentary says, "The guilt offering proclaimed both the need for atonement through blood sacrifice for forgiveness and due restitution toward our brethren in Christ as a demonstration of the sincerity of our repentance" (p.178). This is so true!
If you really want to make peace, ask God to help you breathe grace by humbly and thoroughly admitting your wrongs. One way to do this is to use the Seven A's of Confession by Kenneth Sande from http://www.peacemaker.net/:
1) Address everyone involved (all those whom you affected)
2) Avoid if, but, and maybe (do not try to excuse your wrongs)
3) Admit specifically (both attitudes and actions)
4) Acknowledge the hurt (express sorrow for hurting someone)
5) Accept the consequences (such as making restitution)
6) Alter your behavior (change your attitudes and actions)
7) Ask for forgiveness
See Matthew 7:3-5; 1 John 1:8-9; Proverbs 28:13.
Relationships with others are near and dear to God's heart, and the guilt offering indicates that. Is there anyone with whom you need to reconcile or make restitution?
Lord, thank You that You always make a way back to You through the blood of Christ. Help us to also make our way back to those in which we harbor hurt or resentment (Matthew 5:23-24) or we may have hurt. Make us one in You, Lord. We ask this in Jesus' name. Amen.