TYLER - When exactly did the apostles from the New Testament receive the Holy Ghost? For example, In Acts Chapter 1, before Christ ascended into Heaven, He told them that they would be baptized with the Holy Ghost in a few days.

Acts 1:5, 8-9
5 For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence.
8 But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem , and in all Judaea, and in Samaria, and unto the uttermost part of the earth.
9 And when he had spoken these things, while they beheld, he was taken up; and a cloud received him out of their sight.

A day or so later (Acts 1:15 says “in those days”), the apostles chose a replacement for Judas through revelation.

Acts 1:23-26
23 And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias.
24 And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen,
25 That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place.
26 And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.

Since the event of them being baptized with the Holy Ghost is no doubt an important event, surely it would have been recorded in scripture. The prophecy of it was given by John the Baptist (Matt 3:11; John 1:33) and by Christ in Acts 1:5. Since there is no mention of the gift of the Holy Ghost being given to them between the time that Christ foretold of it and their revelation regarding Matthias, I am assuming that they have not received the gift of the Holy Ghost as of yet but are only going on the influence of the Holy Ghost.
The only event that happens after Jesus foretold of the Holy Ghost coming to them in Acts 1:5 that seems to fit is in chapter 2 of Acts.

Acts 2:1-4
1 And when the day of Pentecost was fully come, they were all with one accord in one place.
2 And suddenly there came a sound from heaven as of a rushing mighty wind, and it filled all the house where they were sitting.
3 And there appeared unto them cloven tongues like as of fire, and it sat upon each of them.
4 And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.

However, what is written in Acts raises a question as to what happened in the gospel of John. Chapter 20 gives us an account of something that happened after the resurrected Christ first appeared to His apostles. John 20:22 "And when he had said this, he breathed on them, and saith unto them, Receive ye the Holy Ghost:"

Did the apostles receive the Holy Ghost before or after His ascension? If they received it according to John, then what Christ said in Acts would not make much sense. I am wondering if there is any information that you could provide to explain this. Additionally, in both accounts there is no information of them receiving the Holy Ghost by the laying on of hands. If they received it from Jesus in John 20:22, then it is most likely this is how it happened even though it is not written. If they received it in Acts 2, then perhaps they received it in a divine manner by the laying on of hands from Christ or heavenly beings and it is not fully explained. Is there any official church doctrine or statement(s) on this subject?

JOEL - First of all I think the "official" interpretation about this from the Church would be, "We don't know exactly how or when the Apostles received the Holy Ghost."
But there have been various scripture based opinions from a few latter-day Apostles on this subject. Here are a few:

Speaking of the John 20:22 scripture where Jesus "breathed on them" President Joseph Fielding Smith said:

"Evidently this was just as efficient as if he had laid his hands upon them.
We discover in the reading of the scriptures that the Lord conferred authority on some of his chosen servants and gave them exceptional powers without the laying on of hands, but merely by his spoken edict. In this manner Elijah obtained the keys of power in the priesthood to raise the dead, heal the sick, close the heavens that it did not rain only by his word, and for more than three years there was no rain, and moreover he had the power to call down fire from heaven to destroy the enemies of the Church.
We may correctly believe that the Lord may bestow the gift of the Holy Ghost by other means than by the laying on of hands if occasion requires it. While it is the practice to lay on hands (Acts 8:15-19), there are many incidents recorded in the scriptures where divine authority has been bestowed by the divine edict to the prophets. (Answers to Gospel Questions, vol. 4, Joseph Fielding Smith)

Bruce R. McConkie said:

"During His mortal ministry our Lord gave His disciples the gift of the Holy Ghost (John 20:22). But as long as Jesus was with them, the actual enjoyment of the gift was withheld (John 7:39; 14:26; 15:26-27; 16:7-15; Acts 1:8). Fullment of the promise came on the day of Pentecost; with miraculous majesty attending," (Acts 2:1-17)(Mormon Doctrine, p. 181)

"In the very nature of things this means that He either conferred the gift upon them by the laying on of hands(but not recorded in the scripture), or He confirmed verbally that He had theretofore given them that gift by the laying on of hands. The gift itself came on the day of Pentecost." (The Mortal Messiah, 4:282)

And by President Harold B. Lee:

"And He "breathed on them, and saith unto them, Receive ye the Holy Ghost:" (John 20:22), which in al likelyhood was the confirmation and the commission to receive the Holy Ghost, by the laying on of hands, for that was the procedure followed thereafter by His Disciples. (Stand Ye in Holy Places, pp. 41-42)

Just before Jesus departed for the last time after His resurrection the scriptures record:

"And, being assembled together with them, commanded them that they should not depart from Jerusalem, but wait for the promise of the Father, which, saith he, ye have heard of me.
For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence. But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth." (Acts 1: 4,5,8)

These scriptures suggest that they had not yet received the gift of the Holy Ghost, even though earlier we are told that He "breathed on them" and commanded them to receive it.

In my opinion I think the act of breathing on them was simply another indication that He was indeed a living, breathing resurected personage. I believe that in the John 20:22 verse, Jesus was giving them permission and a commission to receive the Holy Ghost, but that it did not actually happen until the day of Pentecost. There is the possibility that there was a laying on of hands ordinance performed, but just not recorded (as you suggested). For example we naturally assume that the twelve Apostles were baptized, but nowhere in the scriptures does it specifically record this event.