How do you find diamonds in mine craft?

Answer 1

Diamonds can only be found at the bottom 16 layers of the map, so what you can do is to keep digging down until your y-coordinates (Found by pressing F3 on PC version, and by using a map in Xbox version) and less than 16. Although diamonds are found in all layers, layers 9-12 hold the most amount of diamond.
Strategy:
Mine in a straight line going down (like a staircase) until you are at the top of the bedrock layer (bedrock doesn't come any higher than your feet), and make a 3x3x3 room (3 wide in both x- and z-directions and 3 high). Extend one of the sides (still in a 3 wide, 3 high formation) for as long as you want and then return back to the beginning of the tunnel. Now start making door-shaped holes (1 wide, 2 up) 3 blocks apart on the same wall so it looks like this:
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This is called branch-mining. All you do now is just keep mining in these new door-holes you made until you come across lava, strongholds, caves etc. in a straight line. You get about 4-5 diamonds/30 minutes using this technique. For a more in-depth tutorial, watch this YouTube video. It isn't mine, but it is where I learned how to do it myself, check the related links below.

Diamonds can also be found in chests that naturally spawn in abandoned mineshafts and npc villages.