Itend to find a cave complex and light all/most of it up. Wherein I then dig down with a 3 x 3 x 3 x 3 staircase going down to about layer 10, then I tend to just dig tunnels in three different directions for a ways, connect them and then create a large underground plateau, if you've found a fair few diamonds on your way down you should find loads rather quickly. In the first one I made I found twelve diamonds just building the path, once the plateau was about 12 x 12 3 x 3 boxes, I had well over thirty diamonds(this is without a fortune enchantment). Another great way to find diamonds quickly along with many other ores, is to find a canyon, get to the bottom and if its around 10th - 15th layer you should find loads of diamonds gold and iron all over the place. In this way last one I found, over twenty diamond deposits and ten emerald deposits as well as over two stacks of gold and three stacks of iron without mining and only following paths generated by the game itself. ^-^
The Meaning of Life, the Universe, and Everything.
For my mine I just dug down to level eleven alternating of course so you aren't digging straight down, then you put ladders going back up to the surface with torches so you aren't in complete darkness. Down at the bottom I have a small mining base with a mine heading out in all four directions around 500-1000 blocks in each direction with the mineshafts being two high and 3-5 wide. I also place torches every 8th block in the middle line of the mineshafts to keep them lit up. The best way to mine once you've been on the world for awhile though is to use the Haste II effect of the largest beacon.
I branch mine levels 11-14, meaning 4 block tall tunnels with 2 blocks between them! That covers every diamond from 10 to 15 and if I find any lava it's a block below me so I can just stuff some cobblestone in it! I dunno if it's the best way but it's the best balance for me!
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"Sometimes, I just wanna give up, say 'I'm done with this mess' and go to bed. But you know what; you can't shrug off your responsibilities. You got to pull yourself up and meet the challenges head on. That's the only way you're gonna get ahead in life."
Branch mining @ layer 12. I think branch mining was more effective before the introduction of caves and underground lava (waaay back in the day), 'coz every time you'd inadvertently dig into a cave, chances are you'd get distracted and end off wandering into the cave.
The server I play on has a plug in that creates gigantic caverns down near bedrock. First of all, they are just cool. Secondly, I often find exposed diamonds. Otherwise, I branch mine two high at level ten. Although, looking at that graph I think I will start another branch mine at level 6 under the first one (I will slide it over one block, too). That way I will see most of the blocks in the highest frequecy levels (yes I know that was a terrible sentence).