As you note, the different "millennialisms" are based on different interpretations of the "thousand year reign" mentioned towards the end of Revelation. Unfortunately, answering this question is not as easy as justsimply stating the different views on the millennium itself, because each. Each of the different views only make sense inside their respective theological frameworks. For example, you cannot really taketransplant the a-millennialamillennial view of the millenniumthousand years and stick it insideinto a dispensational theological framework. Thus, in order to properly answer this, we must examine a much broader topicinclude bits of subjects other than just the millennium itself and one must be aware that you cannot simply choose one of these views on their own, you must arrive at one of these understandings based on your hermeneutic for understanding the rest of Scripture.
As you noted, there are several main groupings views on eschatology. Your question mentioned three. While no set of boxes will suffice to accurately categorize these views, I think it's unfair to not include a fourth, namely historic-premillennialism. The modern view called premillennialism is radically different from what was known as premillennialism just a few hundred years ago. The radical shift of views under the same name makes it confusing, so one must delineate.*
The modern iteration of premillennialism is based on dispensational theology and is sometimes knows as Dispensational Premillennialism, although if someone gives no qualification as to which premillennialism is being referenced, it is is generally assumed to be this one.
Also known as "Classic Premillennialism", is actually more similar to Amillenialism than it's modern name-sake. The period of tribulation for the church began with its establishment after the resurrection and will end when Christ returns to earth a second time. Evil will increase in the world along side of good. The church invisible will be sorely tried but always be victorious as protected and strengthened by Christ along the way. There are different views on the great tribulation and whether all of the prophecies are spread out throughout this church age or whether some of them are concentrated into a special great-tribulation period during the last seven (literal or figurative) years at the end. Either way, Christ returns once when the tribulation period is over both to collect his church out of the world, resurrect the dead, and to judge evil. Where historic pre-millennialism differs from amillennialism is what happens after that. Amillennialism sees the thousand years as overlaid on top of the tribulation, parallel tracks as it were or different perspectives on the same event. Historic pre-millennialism believes that the tribulation is now but that after the second return there will be a time of earthly reign in which all things are made new, Christs power to restore is demonstrated on the same turf on which the rest of history was played out but with him physically present and Satan bound. This time can be interpreted as either figurative for a long period of time or a literal thousand years.