The Rambam in Hilchot Melachim discusses the coming of the Mashiach. He is emphatic that nobody really knows for sure what will happen when he comes. We are certain that there is Olam Haba and תחית המתים, the resurrection of the dead.
Some say that all three, Mashiach, Olam Haba, and תחית המתים will all come at the same time. Others, like the Rambam, say that it is a long process that will begin with no שעבוד מלכיות, servitude to other nations. The rest will come over a long period of time.
The Rambam advises that we should support the individual who claims to be the Mashiach. This depends on this person having wonderful character traits and being a great Torah scholar. If he seems that he might have these qualities and he's not a Kohein or Levi, the Rambam tells us to root for him that he is Mashiach.
If he successfully constructs the third Temple, then he is definitely the Mashiach. He will be crowned King of Israel and there will be ingathering of our people. Whatever opinion you follow, know that Mashiach's coming is a great thing for the Jewish people and the world. May he come speedily in our day.