* Who impersonated Moody: Barty Crouch Jr., disguised using Polyjuice Potion.
* What happened: Barty Crouch Jr. (disguised as Moody) took Moody captive and used the Imperius Curse on him to control him. He then used the Polyjuice Potion to take on Moody's appearance. Crouch Jr. used this disguise to infiltrate Hogwarts as a teacher and eventually get Harry Potter selected for the Triwizard Tournament.
* "Killing" Moody: Crouch Jr. never actually killed Moody. Moody was kept in a locked trunk for months, bound and gagged.
It's important to remember that this was a deliberate manipulation by Crouch Jr., designed to get Harry into the tournament. He didn't want to kill Moody, but rather, keep him captive and out of the way.