What's the easiest way to drop an item?
Currently, there is no such shortcut, though there have been many complaints on the D3 forums. Click, drag, click.
Or, if you prefer not to move your wrist, click, I, click to drop, I (open and close inventory).
It is easiest to not drop items and instead use the town portal you are granted relatively quickly in the game. Whenever* you're full, you press T, sell non-magic items, salvage magic items, update your stash as needed and jump right back in action.
*Doesn't work in boss levels until after the boss dies.