Forgiveness starts within your heart and mind. You need to let go of the anger/hate/jealousy ... what ever the negative symptom is that poisons you. Once you've made peace with the wrong doing, you can turn to the person/thing that wronged you. This is the tricky part.
Forgiveness is also mutual... You could forgive <which free's u from hate/anger/jealousy> however, the person you're forgiving may not want to be forgiven. Example ... your spouse may have cheated on you and does not want forgiveness. They would rather get a divorce and they wanted to hurt you. See, forgiveness isn't mutual here. You still need to find that place where you rid yourself of negativity, and remove yourself from the person who does not want forgiveness.
Religion does a great job of teaching us about forgiveness. Confessions are one of the first lessons we get about forgiveness. Three acts are required from the Penitent <us sinners who WANT to be forgiven> for forgiveness through the sacrament of confession. These are Contrition, confession, and satisfaction.
Contrition is sincere sorrow for having offended God, the most important act of penitent. There can be no forgiveness of sin if we do not have sorrow and a firm resolve to not repeat our sin. See if we were married and cheated on our spouse the first step is for us to feel sorry that we cheated and to resolve in our heart not to cheat again; flip side, if your spouse has cheated on you, they willing have to be sorry and willingly have to resolve not to cheat on you again.
Confession requires confronting our sins in a profound way before God by acknowledging them aloud to a priest. The priest is a conduit to God in confession. In the marriage if you cheated on your spouse, you must go to the spouse and inform them of the affair; flip side, if your spouse cheats on you, then they need to come to you ... hiring a private detective leads you down a path where you'll forgive but they aren't ready to be forgiven.
Satisfaction is the "penance" the priest imposes on the penitent to make amends for sin, an important part of our healing. Once you've cheated on your spouse, you need to make it up to your spouse <give up your computer/phone/whatever caused you to stray>; flip side, if your spouse cheated on you, they need to give up whatever was the temptation to lead them to stray.
In today' Western culture, it seems that cheating spouses don't heal because they don't work their way through the basic forgiveness techniques <Contrition, Confession, and Satisfaction>. Instead most are stuck at level 1: Contrition. If the couples make it to level 3 "Penance" then victim spouse usually does not have the courage to require a healing penance to their spouse.