a bishop’s court will include the bishop, his two counselors and the ward clerk who will record the proceeding. He can impose any of the following: no action, informal probation (the person will have regular meetings with the bishop until he decides everything is okay), formal probation (same thing but documented), disfellowhiped (member can hold no callings, can’t take the sacrament {communion}, can’t pray publicly in church [on behalf of the group like invocations] and if male cannot exercise any priesthood authority, or excomunication (no longer a member)
if the person is a male and a melchizadec priesthood holder (most adult LDS men are) then the bishop must refer it to the stake president who MAY allow the bishop to handle it the person is cooperative and agrees to that, otherwise the court is in front of the stake high council where teh stake president, his counselors, the various stake high councilmen and the clerk are present.
in both cases after the person “confesses” to the group they are able to ask questions until all are prepared to render a decision. teh person then leaves the room and the court deliberates. the final decision will then be made by the bishop or stake president. the person returns to the room and is informed of the decision.
if a person was disfellowshipped they will meet with their bishop until the bishop or stake president approves the being restored to full fellowship.
If excommunicated they will have to be rebaptized after at least a year and requiring approval. if a melchisadec priesthood holder the rebaptism only restores their membership, temple blessings, priesthood etc. must be restored later in a temple ordinance called restoration of blessings that requires approval from the first presidency of the church.
there is no absolution equivalent only an end to disciplinary action. all of it is documented in your permanent membership records.