how to get back into church after you've been kicked out

This is really part B of the idolatry topic from yesterday. A return to idolatry happened en masse a few times in the history of the early church when the Roman emperors tried to crush Christianity. They are called the lapsi.

The regular designation in the third century for Christians who relapsed into heathenism, especially for those who during the persecutions displayed weakness in the face of torture, and denied the Faith by sacrificing to the heathen gods or by any other acts. Many of the lapsi, indeed the majority of the very numerous cases in the great persecutions after the middle of the third century, certainly did not return to paganism out of conviction: they simply had not the courage to confess the Faith steadfastly when threatened with temporal losses and severe punishments (banishments, forced labor ... death), and their sole desire was to preserve themselves from persecution by an external act of apostasy, and to save their property, freedom, and life.

When things got hot, they withered, as Jesus predicted in the parable of the soils, Luke 8:13. Jesus says they have no root. They weren't completely rejected by the church, and they didn't seem to get the treatment the guy in Corinth got, of whom Paul wrote in 2 Corinthians 2,

6 This punishment on such an individual by the majority is enough for him, 7 so that now instead you should rather forgive and comfort him. This will keep him from being overwhelmed by excessive grief to the point of despair. 8 Therefore I urge you to reaffirm your love for him.

In the 4th century the process of public penance was tough.

The first question, therefore, was whether the Sacrament of Penance can effect a reconciliation whereby the apostate, or in some cases specifically the traditor, may be returned to full communion. The orthodox Catholic position was that the sacrament was for precisely such cases, though at the time the Church still followed the discipline of public penance whereby a penitent for such a grievous offense would spend years, even decades, first outside the doors of the church begging for the prayers of those entering, then kneeling inside the church building during services, then standing with the congregation, and finally receiving the Eucharist again in a long progress toward full reconciliation. The Donatists held that such a crime, after the forgiveness of Baptism, rendered one unfit for further membership in the Church, a position of extreme rigorism.

It's amazing in our time today to think the Donatists weren't satisfied. The Catholics and Orthodox have two different formal procedures for reconciliation with the church. Protestants usually disentangle confession from fruits of repentance, which could be why the church appears so weak. However, it's not like any church seems very strong, except for the heavy handed legalistic, soul-destroying churches. The article on public penance at wikipedia is amazing in its useful brevity.

Catholic

In the Catholic Church, the sacrament of Penance consists of three parts: contritio, confessio and satisfactio.

Contritio is in fact repentance as Protestant theologians understand it, i.e. love of God causing sorrow for sins committed, and long before the Reformation the schoolmen debated the question whether complete "contrition" was or was not in itself sufficient to obtain the Divine pardon. The Council of Trent decided, however, that no reconciliation could follow such contrition without the other parts of the sacrament, which form part of it (sine sacramenti voto, quod in ilia indudatur). Contrition is also distinguished from "attrition" (attritio), i.e. amoral repentance due to fear of punishment. It was questioned whether a state of mind thus produced would suffice for obtaining the benefits of the sacrament; this point was also set at rest by the Council of Trent, which decided that attrition, though not in itself capable of obtaining the justification of the sinner, is also inspired by God and thus disposes the soul to benefit by the grace of the sacrament.

In this Sacrament, the penitent (repentant sinner, known as confessant) accuses himself of his sins to an ordained priest (known as confessor). The priest may then offer advice and imposes a particular penance to be performed. The penitent then prays an Act of Contrition, the priest administers absolution, thus formally forgiving the penitent of his sins, and finally sends him out with words of dismissal. Often, penitential acts consist simply of prayers, fasting, charitable work or giving, or a combination thereof. Such penance is frequently accompanied by a requirement for the penitent to be reconciled with anyone against whom he or she has sinned.

Orthodox

In Roman Catholicism, the goal of the sacrament of Penance is reconciliation with God, through means of justification. However, in Orthodoxy, the intention of the sacramental mystery of Holy Confession is to provide reconciliation with God, but through means of healing.

Similar to the Eastern Catholic Churches, in the Eastern Orthodox Church there are no confessionals. Traditionally the penitent stands or kneels before either the Icon of Christ the Teacher (to the viewers' right of the Royal Door) or in front of an Icon of Christ, "Not Made by Hands". This is because in Orthodox sacramental theology, confession is not made to the priest, but to Christ; the priest being there as a witness, friend and advisor. On an analogion in front of the penitent has been placed a Gospel Book and a Crucifix. The penitent venerates the Gospel Book and the cross and kneels. This is to show humility before the whole church and before Christ. Once they are ready to start, the priest says, “Blessed is our God, always, now and ever, and unto the ages of ages,” reads the Trisagion Prayers and the Psalm 50 (in the Septuagint; in the KJV this is Psalm 51).

The priest then advises the penitent that Christ is invisibly present and that the penitent should not be embarrassed or be afraid, but should open up their heart and reveal their sins so that Christ may forgive them. The penitent then accuses himself of sins. The priest quietly and patiently listens, gently asking questions to encourage the penitent not to withhold any sins out fear or shame. After the confessant reveals all their sins, the priest offers advice and counsel. The priest may modify the prayer rule of the penitent, or even prescribe another rule, if needed to combat the sins the penitent struggles most with. Penances, known as epitemia, are given with a therapeutic intent, so they are opposite to the sin committed.

Epitemia are neither a punishment nor merely a pious action, but are specifically aimed at healing the spiritual ailment that has been confessed. For example, if the penitent broke the Eighth Commandment by stealing something, the priest could prescribe they return what they stole (if possible) and give alms to the poor on a more regular basis. Opposites are treated with opposites. If the penitent suffers from gluttony, the confessant’s fasting rule is reviewed and perhaps increased. The intention of Confession is never to punish, but to heal and purify. Confession is also seen as a “second baptism”, and is sometimes referred to as the "baptism of tears".

In Orthodoxy, Confession is seen as a means to procure better spiritual health and purity. Confession does not involve merely stating the sinful things the person does; the good things a person does or is considering doing are also discussed. The approach is holistic, examining the full life of the confessant. The good works do not earn salvation, but are part of a psychotherapeutic treatment to preserve salvation and purity. Sin is treated as a spiritual illness, or wound, only cured through Jesus Christ. The Orthodox belief is that in Confession, the sinful wounds of the soul are to be exposed and treated in the "open air" (in this case, the Spirit of God. Note the fact that the Greek word for Spirit (πνευμα), can be translated as "air in motion" or wind).

Once the penitent has accepted the therapeutic advice and counsel freely given to him or her, by the priest then, placing his epitrachelion over the head of the confessant. The priest says the prayer of forgiveness over the penitent. In the prayer of forgiveness, the priests asks of God to forgive the sins committed. He then concludes by placing his hand on the head of the penitent and says, “The Grace of the All-Holy Spirit, through my insignificance, has loosened and granted to you forgiveness.”

In summary, the Priest reminds the penitent what he or she has received is a second baptism, through the Mystery of Confession, and that they should be careful not to defile this restored purity but to do good and to hear the voice of the psalmist: “Turn from evil and do good” (Psalm 34:14). But most of all, the priest urges the penitent to guard him- or herself from sin and to commune as often as permitted. The priest dismisses the repentant one in peace.

Protestant

The Reformers (e.g. Puritans), upholding the doctrine of justification by faith, held that repentance consisted in a change of the whole moral attitude of the mind and soul (Matthew 13:15; Luke 22:32), and that the divine forgiveness preceded true repentance and confession to God without any reparation of "works." As Calvin says in his piece Of Justification By Faith: "without forgiveness no man is pleasing to God." Rather, "God's kindness is meant to lead you to repentance" (Romans 2:4, ESV); nonetheless, there has traditionally been a stress on reconciliation as a precondition to fellowship.

As a Protestant I admit I am partial to the Reformers position. I like the 12 steps in AA.

• admitting that one cannot control one's addiction or compulsion;
• recognizing a greater power that can give strength;
• examining past errors with the help of a sponsor (experienced member);
• making amends for these errors;
• learning to live a new life with a new code of behavior;
• helping others that suffer from the same addictions or compulsions.

That sounds like public confession, submission to God, personal accountability, demonstrated fruits of repentance, repentance, and discipleship. Perhaps Paul would say the first 5 happen before the offender returns to fellowship.