This is pretty easy, when I play, I only do so with my PS3 controller.
I'll break it out into arbitrary steps for you based on my PS3 controller setup, and you have to figure it out from there:
1) Connect your controller to your computer, this typically requires the right software that can install the drivers needed for your controller, like MotioninJoy.
2) You need to map keyboard keys and mouse movement/clicks to your controller, MotioninJoy has an option labled "custom", this is the one you want to use, when selecting the controller button, you have to select "keyboard" or "mouse" from the dropdown menu and selecting which button/click/movement you want to be mapped to which controller button.
3) You're almost done, most people stop there since the keys are mapped and the game is playable, for example I map RMB to R1 and mouse movement to the right analog stick, so that way I can move my character around with relative ease, but I also use a hotkey macro that lets me move in WASD movement from the left analog stick. You need to do some searching around for software that lets you auto-hotkey ;). There are some scripts floating around the interwebs that map keyboard buttons to mouse positioning and clicking (simulating if you move the mouse above your character and click to move them north, etc.)
I would put the exact links and things for you but who knows. Blizz doesn't want you to have fun, only to prescribe to their vision of a "PC mouse click game", but here is a link that shows this is possible:
I would worry about getting banned for doing this, except the PS4 version is right around the corner, so Blizz really doesn't have a good reason to disallow WASD movement on PC vs PS3/360/PS4 titles.
Edited by ShoknAwe#1176 on 4/16/2014 12:54 PM PDT