How to find diamonds (no cheating)
10 diamonds
Diamond caches are randomly dispersed within 16 blocks of the bottom of the map. As long as your Y coordinate is less the 16 (press F3 to see the exact position), your likelihood of finding diamonds is the same as anywhere else. Deeper isn't better: once you hit the 16-mark, it's the same no matter how deep you go.
Deposits contain more diamonds on average in the southwest quadrant of the map due to a bug.
The entropy of the randomness is close to one. What this means is that you will rarely find two diamond caches near each other. Once you find a diamond cache, move at least 16 blocks away before searching again. There is exactly one diamond cache per chunk.
The cave network in Minecraft is infinite. Use this to your advantage: rather than digging, follow the caves. You will cover much more area in a shorter time.
If you have access to TNT, use it. Mine long, straight tunnels, then place TNT every five blocks or so. Kaboom! If you're lucky, you'll expose a diamond cache. Be sure to check your tunnels for diamonds along the edges before blowing it up, though.
Once you get diamond, use it to find more diamond. Diamond tools are an investment. The increased speed at which you will locate diamond will pay for the diamond tools rather quickly.
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