The fastest way is to find an abandoned mineshaft that extends deep enough (below layer 17). They reveal a lot of blocks, and you can also find diamonds in the chests. They're kind of a rare occurrence though so your best bet is to strip mine at y=13.
Diamonds occur at level 16 and below, however, bedrock begins to appear at level 6 and below, meaning it's best to search between these 10 levels. I have found that diamond mostly commonly occurs between levels 8 and 12, so producing a shaft mine is the best method.
This is achieved by starting to dig a tunnel at level 6, making it 1 block wide, about 4 blocks tall and keep going for about 10 blocks. If you find nothing, head back out and go down two blocks and start a new tunnel with the same dimensions. Now you should have two 1 x 10 x 4 tunnels two blocks apart. This maximises the chances of finding diamond as you are exposing new blocks with every tunnel. Do this for each cardinal direction, so you have a small central area to come back to and store or smelt ores. With this method I often find quite a few.
Alternatively you could start at level 6 and just dig out a massive chamber in all directions. This is most time consuming but yields more diamonds. I currently have a 200 x 200 x 4 chamber under my house where I have found 3 full stacks of diamonds.
Diamonds spawn between the Coordinates of Y: 1-16*
Take note that on levels 1-4 bedrock always spawns soo branch mining is there by ineffective"
its up to you to decide what level to mine but also take note if you branch mine you will discover Lava pits and caves quite frequently and I do suggest going into caves is that is where I always find my first diamonds then I branch mine out from there.
Also to let you know the best layers to find diamonds are Y: 5-13
and diamonds can be found in:
If you dont know how to branch mine all you have to do is go to youtube and type in Branch mining tutuorial *thats how I learned* and If you want to there is also How to find diamonds tutorials out there, You can learn completely how to play minecraft from youtube
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"Belief will change my world it has moved continents and countries and it has put man on the moon and it will carry me through this battle."
The Darkness will win one day, and light's time being the winner is nearing it's end. Because light is overrated.
IntelliJ > Eclipse because better autocomplete and inbuilt command line. Oh, and use the latest version for mods.
My heavily work in progress Minecraft Modding API and mod loader, N-API: https://github.com/Niadel/N-API
Code changes from 1.7 to 1.8 for us modders (that I found): https://gist.github.com/Niadel/2d2db8dd89de27f970a7