What happens to Professor Moody in Harry Potter and the Goblet of Fire?

What happens to Prof. Moody in Goblet of fire?

Well, he was kidnapped and imprisoned in the box by the Barty Crouch JR. And Barty needed him to keep his appearance as Moody intact.

In the end, Snape used Verataserum to make him tell the truth. He and Prof. Dumbeldore found him in that box and rescued him.

After he was rescued, he was, of course, free.

And how does he come back to rescue Harry in Order of Phoenix?

Since now he is free and Harry needs to be kept safe, he comes back in The Order of the Phoenix along with others.

In Goblet of Fire, the real Moody was essentially kidnapped/taken hostage by Barty Crouch Jr., who then impersonates him using Polyjuice Potion. Barty Crouch Jr., who is a Death Eater (i.e. one of Voldemort's supporters), does this in order to get close to Harry, who he uses as a pawn to help revive Voldie. You can read the SparkNotes summary, if you like. You'll likely find this quote - which describes a scene towards the end of the movie - to be most useful:

Once Harry returns, he is weak and shaken. Moody carries him into the castle, where Moody reveals that he is in fact a Death Eater, and that he was responsible for placing Harry's name in the Goblet and for turning the trophy into a portkey. Moody also informs Harry that Karkaroff felt his Dark Mark burn and then fled that night. Moody prepares to kill Harry when Dumbledore and other teachers burst into the room, stunning Moody and saving Harry. Dumbledore explains to Harry that Moody's body is a disguised version of Mr. Crouch's son, the young Barty, and that he has made the switch by drinking Polyjuice potion every hour. After some time, the potion wears off and Harry recognizes Barty Crouch.

By the end of that book/movie, Barty is discovered for who/what he really is, and the real Moody - who Barty needed to keep alive as a hostage for the purposes of his Polyjuice Potion - is freed from the magical cell that Barty had been keeping him in. (Barty was keeping Moody in what was essentially a makeshift cell inside an enchanted trunk.) So he can come back in the next movie/book because he wasn't actually hurt in a way that he couldn't recover from. (Plus, the real Moody is quite the opposite of Barty Crouch Jr, and prefers to fight against Voldie, rather than for him.)