I would like to start this out by stating that this is for those who do not know this and would like to learn.
Your first step is to look up your character in the "armory." To do this you'll need to go to World of Warcraft (US) or World of Warcraft (EU), depending on your location. You're then going to need to search your character's name and find it through the list of names you are given. This is easily done through sorting filters, (Sorry if this doesn't make sense; I am very tired.), such as realm name alphabetically and name alphabetically. Click your character's name and you should get a screen that shows both your gear and your character. Right click on your character and click "View background image." then you should get a picture of just your character. You can either right click and save the image, or right click and set it as your desktop background.
I hope you enjoyed this and enjoy your new wallpaper!