MELONI - I came across john 20:23 where Jesus gave his apostles the power to decide whose sins could be forgiven or should be retained.

John 20:23 - Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.

I am aware that Jesus forgave sins and had the authority from God to do so. He was a member of the Godhead and it would seem fitting. I imagine if he gave them the authority to do the same, it is not up to us to question. However, I was wondering if the apostles today have this same authority and how is it possible to be forgiven by them rather than by God Himself?

JOEL - Jesus ordained His Apostles(John 15:16) and gave them the priesthood keys and authority so that whatever they would bind on earth would be bound in heaven(Matt 16:19). They could stand in His place and perform the ordinances that are necessary for the remission of the sins and salvation(eg. baptism), but they personally could not forgive the sins; only God can do that.
Jesus gave our latter-day Apostles and Prophets the same authority:

"And verily, verily, I say unto you, that whatsoever you seal on earth shall be sealed in heaven; and whatsoever you bind on earth, in my name and by my word, saith the Lord, it shall be eternally bound in the heavens; and whosesoever sins you remit on earth shall be remitted eternally in the heavens; and whosesoever sins you retain on earth shall be retained in heaven." (D&C 132:46)

Once again these scriptures do not mean that the Apostles can forgive someone of their sins, however God's ordained servants can participate in the sin remission process. There is a difference between remission of sins and forgiveness of sins, although both are required for salvation. Remission of sins is accomplished through the ordinance of baptism. With the authority from God and by obedience to the laws and ordinances of the gospel, sins are washed away in the waters of baptism and sin is removed from souls as though by fire when people are baptized by the Holy Spirit. In this way those who have the authority to perform these ordinances, have power to remit the sins of men in the waters of baptism, or they have power to retain the sins of those who do not repent and are not baptized for the remission of sins.