It really confuses me that a man like Tom Riddle, who goes on to become one of the most feared Dark Wizards around, would ever be interested in teaching a bunch of young children how to fight the Dark Arts. Why did Voldemort want to teach the Dark Arts so much?
This is covered in great detail in chapter 20 of Half-Blood Prince. First of all, there's some evidence to suggest that he didn't want it and instead only wanted to go back to Hogwarts.
"Let us speak openly. Why have you come here tonight, surrounded by henchmen, to request a job we both know you do not want?"
Voldemort looked coldly surprised. "A job I do not want? On the contrary, Dumbledore, I want it very much." "Oh, you want to come back to Hogwarts, but you do not want to teach any more than you wanted to when you were eighteen. What is it you’re after, Tom? Why not try an open request for once?"
Voldemort sneered. "If you do not want to give me a job —"
"Of course I don’t," said Dumbledore. "And I don’t think for a moment you expected me to. Nevertheless, you came here, you asked, you must have had a purpose."
Voldemort stood up. He looked less like Tom Riddle than ever, his features thick with rage. "This is your final word?"
"It is," said Dumbledore, also standing.
"Then we have nothing more to say to each other."
But Dumbledore contradicts this at the end of the chapter:
"Oh, he definitely wanted the Defense Against the Dark Arts job," said Dumbledore. "The aftermath of our little meeting proved that. You see, we have never been able to keep a Defense Against the Dark Arts teacher for longer than a year since I refused the post to Lord Voldemort."
The ultimate explanation seems to be the one given to us by Dumbledore earlier on in this chapter:
"Firstly, and very importantly, Voldemort was, I believe, more attached to this school than he has ever been to a person. Hogwarts was where he had been happiest; the first and only place he had felt at home." [...]
"Secondly, the castle is a stronghold of ancient magic. Undoubtedly Voldemort had penetrated many more of its secrets than most of the students who pass through the place, but he may have felt that there were still mysteries to unravel, stores of magic to tap.
[sic, my copy doesn't close the quotation marks before opening these next ones]
"And thirdly, as a teacher, he would have had great power and influence over young witches and wizards. Perhaps he had gained the idea from Professor Slughorn, the teacher with whom he was on best terms, who had demonstrated how influential a role a teacher can play. I do not imagine for an instant that Voldemort envisaged spending the rest of his life at Hogwarts, but I do think that he saw it as a useful recruiting ground, and a place where he might begin to build himself an army."