To locate dungeons easily, have plenty of torches and some weapons, just in case you encounter a monster. Go to an area that you think may have dungeons. Make sure that area is well-lit with torches, just in case night falls (if it has not already.) Press to open up the menu. Enter the "Options" menu and change the difficulty from "Peaceful" (or whatever difficulty you are on) to "Hard". Close the menu and press . ID numbers will appear on top of each animal or monster in range. Look towards the ground and search for an unusually large concentration of ID numbers underground; this is more than likely a group of monsters. It will either lead you to a cave or, more fortunately, a dungeon.
This trick works best on slow computers, but it is also not fully reliable. If you are in an area where you think a dungeon may be near, press F (you may need to press it repeatedly). Look around while pressing it. If you see flames showing up while the screen is blue (the sky), it indicates there is a dungeon within sixteen blocks of you. Note: This method only works when a dungeon is sixteen blocks near.