Revelation 20 speaks of a 1000 year period, or another name for it is a millennium.
One example verse is:
2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years,
Amillennialism is the belief that this period is not a literal 1000 years, but figurative, and that this period is the current gospel age, which will afterward be followed by Satans little season, then God coming to judge the earth, separating believers to be with Him, and unbelievers to go to eternal judgement.
Well we need to look at the context. The period is mentioned in Revelation, which is a symbolic book through and through. Even in this chapter, we have a chapter full of symbols. We read about a key to the bottomless pit, which clearly isn't literal. Satan is spiritual, so cant be locked away with lock and key. We read about a seal being set on him, which clearly wasn't a literal seal. It just symbolises that God has decreed it, and it's set in stone.
The 1000 year period is symbolic too.
So to start with, we read verse:
3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.
Satan was cast into the bottomless pit till the end of the 1000 years, and then was loosed for a little season. So we have an order here, the millennium, then Satans little season. And again this order is backed up in verse:
7 And when the thousand years are expired, Satan shall be loosed out of his prison,
So Satan will be loosed at the end of the 1000 years for a short time.
Then after this short time we read on, and read about Christs glorious second coming:
11 And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them. 12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
So order is, millennium, Satans little season, and then Christs second coming. As everywhere else in the bible, so here, we have Christs glorious return followed by the final judgement.
13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
So the order is even clearer now.
Millennium, Satans little season, Second coming, and resurrection of all the dead, final judgement.
We don't need to reverse the order it's given to us in the bible. We simply take Revelation 20 as it is.
Well let's look at verse 3 again. The event that starts this millennial period was the binding of Satan, particularly in conjunction with being able to decieve the nations no more.
Well, verses such as:
Luke 10:17 And the seventy returned again with joy, saying, Lord, even the devils are subject unto us through thy name. 18 And he said unto them, I beheld Satan as lightning fall from heaven.
Clearly show us that from Christs first coming, Satan was bound up in a way that he hadn't been before. This was also in conjunction with deceiving the nations no more. Christs death was followed closely by the gospel age, where the gospel was taken to all nations. The day of pentecost and speaking in tongues was a sign to show this. Up till this point, God had worked in a special way with the Jewish nations, but from now on He was pulling individuals out of all nations.
So this millennium period runs all the way from Christs first coming up to Satans little season, which won't last for long, and then Christ will return again.
One final thing to tie up:
4 And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.
So believers were reigning for 1000 years with Christ, so where and how was this happening? Well this verse tells us it is the souls that were reigning with Christ. So this is a spiritual thing, happening in a Spiritual place, not something physical on Earth.
We know that souls don't remain on earth, they go to heaven, so the reign is in heaven. This is backed up by the picture of thrones, which through revelation are found in heaven.
Secondly, the fact that the verse speaks of sous and not bodies tells us that this period ends with Christs second coming. When Christs comes again, we know that believers will have a body as well as a soul. Read 1 Corinthians 15 to see that. So this period will end when Christ comes again and believers have a body and soul again.