basic facts;

Name: Alastor Moody
Nickname: Mad-Eye, because of his magic eye, which is able to see even through the walls... and the invisible cloaks ;)
Age: unknown. I've always thought he would be fifty-something, though.
Job: he was an Auror (a dark wizard catcher), actually it's said he was the best Auror the Ministry ever had, but he is retired now. In Goblet of Fire he's the new professor of Hogwarts in Defense Against the Dark Arts. In Order of the Phoenix, he's one of the most important members in the Order and one in the chosen group of people who go and take Harry from the Dursley's to the order headquarters, in the beginning of the book.

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"A man stood in the doorway, leaning upon a long staff, shrouded in a black traveling cloak. Every head in the Great Hall swiveled toward the stranger, suddenly brightly illuminated by a fork of lightning that flashed across the ceiling. He lowered his hood, shook out a long mane of grizzled, dark gray hair, then began to walk up toward the teachers' table.

A dull clunk echoed through the Hall on his every other step. He reached the end of the top table, turned right, and limped heavily toward Dumbledore. Another flash of lightning crossed the ceiling. Hermione gasped.

The lightning had thrown the man's face into sharp relief, and it was a face unlike any Harry had ever seen. It looked as though it had been carved out of weathered wood by someone who had only the vaguest idea of what human faces are supposed to look like, and was none too skilled with a chisel. Every inch of skin seemed to be scarred. The mouth looked like a diagonal gash, and a large chunk of the nose was missing. But it was the man's eyes that made him frightening.

One of them was small, dark, and beady. The other was large, round as a coin, and a vivid, electric blue. The blue eye was moving ceaselessly, without blinking, and was rolling up, down, and from side to side, quite independently of the normal eye - and then it rolled right over, pointing into the back of the man's head, so that all they could see was whiteness"

(Goblet of Fire, chapter twelve: The Triwizard tournament)

This is the physical description of Mad-Eye Moody we can find in GoF (no wonder why Harry and the others think at first he's quite scary...), though the first time we know about him is in the previous chapter. Arthur Weasley gets an important message from the Ministry about some strange things around Mad-Eye Moody: it seems that someone tried to break into his house last night...

Moody was a very capable auror in the past, but now in his old age he's becoming really paranoid: he doesn't trust anyone (he always drink from his own hip flash, because he thinks anyone could poison him), and he sees dark wizards everywhere. He also seems to be particularly worried about wand safety, something that maybe could have something to do with his own missing leg.