How do I find diamonds?

When in doubt, Find a Cave.

If you don't see anything on the surface, Dig Deeper.

Really, that's all there is to it. In general, you won't find Diamond much past 10 levels or so above Bedrock.

The graph below (taken from TR's interactive MC Block Distribution Chart) shows the density of Diamond in one generated world. 0 on the X axis represents bedrock. 255 is the top of the sky.

Follow a path that's been previously mined out by water. All you have to do is replace the source block (the block from which water appears to be flowing), and the water will cease to flow, allowing you easy passage through the cave.

After you've stopped the flow of water, follow its former path. Not only will your path be carved out for you, but you'll be much more likely to find coal, gold, red ore and diamond.

One way I find lots of diamond is by making something I called Mining rooms. How you do this is dig a staircase type thing down until you're a couple blocks above bedrock. When you get there dig as far as you can right without moving and do the same thing to the left (your tunnel should look sorta like a "T" by now). Go into the right tunnel and dig a tunnel to the left(as long as you want). You then dig 9 blocks to the left. when you do that turn to the left once more and dig until you find your tunnel. Then dig up all the area in between the tunnels. Using this strategy I found 30 diamonds, 75 redstone, 36 iron, and loads of coal within an hour. Hope this helps