From an LDS perspective, what is the difference between feeling the influence of the Holy Spirit and receiving the gift of the Holy Spirit? What is the difference between the two? What scriptures are used to best explain the differences? How does one receive the gift of the Holy Spirit?
Joseph Smith taught:


  There is a difference between the Holy Ghost and the gift of the Holy
  Ghost. Cornelius received the Holy Ghost before he was baptized, which
  was the convincing power of God unto him of the truth of the Gospel,
  but he could not receive the gift of the Holy Ghost until after he was
  baptized. Had he not taken this sign or ordinance upon him, the Holy
  Ghost which convinced him of the truth of God, would have left him.
  [See Acts 10:1–48.] Until he obeyed these ordinances and received the
  gift of the Holy Ghost, by the laying on of hands, according to the
  order of God, he could not have healed the sick or commanded an evil
  spirit to come out of a man, and it obey him; for the spirits might
  say unto him, as they did to the sons of Sceva: ‘Paul we know and
  Jesus we know, but who are ye?’ [See Acts 19:13–15.]


History of the Church, 4:555; from a discourse given by Joseph Smith on Mar. 20, 1842, in Nauvoo, Illinois; reported by Wilford Woodruff.