The rapture doctrine's origin is usually credited to John Nelson Darby, he had written down this theology by 1827. (1800-1882). There has been a story around that the rapture doctrine came from the "utterances" of Margaret McDonald in a Scottish church about 1830. More than likely she was just repeating what she had heard from John Darby. This is a complete assumption on my part since Darby had written these things down 3 years earlier and they were in proximity of each other.
There are six key parts to the premillennial doctrine of the rapture.
(1) The "second coming" of Christ is different from and after "the rapture," we believe the Bible distinguishes between the rapture and the second coming of Christ and they do not occur simultaneously. (Hal Lindsey's book 131)
(2) The rapture will be secret, "in the rapture, only the Christians see Him - its a mystery, a secret. When the living believers are taken out, the world is going to be mystified." (Ibid 131)
(3) Only the righteous will be raised at the time of the rapture. The wicked will be raised at the end of "the millennium."(Ibid 130-31)
(4) The church will be in Heaven for a period of seven years (during the Great Tribulation). "your presence during this last seven-year period in history is entirely up to you."(Ibid 127)
(5)Events on earth will continue. "These believers will be removed from the earth before the Great Tribulation - before that period of the most ghastly pestilence, bloodshed, and starvation the world has ever known."(Ibid)
(6) Many will be led to Christ after this. "We need to understand that during the seven-year Tribulation there will be people who will become believers at that time."(Ibid 132)
What the Bible says.
Referencing the first key part:
For the second coming of Christ the Bible uses the words "caught up" (harpazo or rapture by premillenialist), "coming" (parousia) and "appearance"(epiphaneia) interchangeably. The Lord will destroy the lawless one "with the brightness (epiphaneia) of his coming (parousia). (2 Thessalonians 2:8)....This "coming" (parousia) is at the same time he catches up (raptures) the saints. (1 Thessalonians 4:15,17) Jesus won't return a third and a fourth times; there's just the second coming. These events Christians being "caught up" and the second coming of Christ, are not separated by 1007 years (1000 year reign and 7 year tribulation), as premillennialists contend, but they will happen at the same time.
Referencing the second key part:
When he comes for the saints there won't be anything secretive. "For the Lord himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God." (1 Thessalonians 4:16). "The day of the Lord will come as a thief in the night, in which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat. The earth and works therein shall be burned up." (2 Peter 3:10)
Nothing quiet here, the voice of an archangel, and the trumpet of God, also the heavens are going to pass away with a great noise. All this when the Lord returns. The secretive part of the premillienialists comes from the phrase, "come as a thief in the night", which just simply means they you don't know when he's coming. Another example of this comes from Matt. 24:43. Another good example is 1 Thessalonians 5:1-4.
Referencing the third key part:
"Do not marvel at this; for the hour is coming in which ALL who are in the graves will HEAR his voice and come forth, those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of damnation." (John 5:28-29)
Referencing the fourth, fifth and sixth key parts:
There will be no fourth, fifth and sixth parts. "For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trumpet of God. And the dead in Christ will rise first. Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air. And thus we shall ALWAYS be with the Lord." (1 Thessalonians 4:16-17) Scripture plainly says we won't be with the Lord seven years. We will always be with the Lord after his second coming. There aren't any other "comings". At his coming (parousia) the earth will be destroyed, 2 Peter 3:1-12. There will be no second chance to be saved then, for at His coming all shall be judged and receive either eternity in heaven or in hell, Matt. 25:31-46. Call his coming what you will, "second coming" or "rapture", either way he's only coming back one more time. We need to know that and be ready.