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With everyone being so helpful, I can't imagine what I could contribute, but I'll try my best.
Short Answer: The best way to get diamonds (in 1.2.5) is to mine (or explore caverns) while standing on the sixth block up from the highest level of bedrock (hitting F3 should show your Y-coordinate as ~12.6).
Longer Answer: These are just tips I've picked up from the Wiki and elsewhere, and it's pretty much how I mine for diamonds:
Make a shaft for rapid descent: You want to be able to move up and down as quickly as possible, and I believe this method is the best at balancing speed and expense:
Dig a 3x1 vertical shaft down to the bedrock (never dig the block directly below you: keep switching sides as you head down).
Put ladders on one end of the shaft (this will be your ascent shaft).
Fill in the middle of the 3x1 shaft with a tower of cobblestone, turning your 3x1 shaft into two 1x1 shafts. Leave a 2-block-tall gap at the bottom so you can move between shafts.
In the shaft without the ladders, place a sign on the wall three blocks up from the bottom, then dump a single block of water above the sign (it will "hover" there; this will be your descent shaft).
You can now free fall from sea level to bedrock in less than a second, because the water block hovering above the sign will break your fall.
You'll fall into a 1x1, 3-block-tall gap at bedrock level, just below the hovering water block, perfect for digging hallways.
From here on out, watch for lava: More than once while I was digging out my base, I hit a lava pool and had to scramble for buckets of water (while scaring the hell out of my dog).
Make a bedrock base: Dig out a room and fill it with chests, a crafting table, three furnaces, an incinerator (one block of lava) and an infinite water source.
Infinite Water Source: Dig 3 blocks in an L-shape at one corner of the room, with the "bend" of the L being the only part that juts into the room (the other two blocks should be dug out from under the walls, where they meet at the corner). Then, put two water blocks at the ends of the L, under the walls—the bend between them becomes an infinite water source that takes up only one block in your room.
I recommend no bed here. Put it at the top of your mine shaft instead: Descent is so rapid that you don't need to respawn at bedrock level.
Dig a staircase to Y = 12: Find the highest level at which bedrock spawns (there are five levels of bedrock), then dig a staircase up six blocks. At this level, hitting F3 should show your head to be at Y=12.6 (-ish). Your feet are standing on Y=11.0, and the block you're standing on (which will be the floor of your mining tunnels) occupies all of Y=10.
This means the floor of your mining tunnels also happens to be the laval level, so be careful, and bring water to obsidiafy any lava you encounter.
Mine. Dig a 2-block-high mining corridor off in any direction, keeping your head at Y=12.6 (-ish). To keep your base close, instead of digging infinitely, dig branching tunnels off from your main corridor every six blocks.
Because ore forms in clumps/veins, digging parallel branch tunnels separated by less than 6 blocks means you'll overlap veins you already saw from other tunnels. (Don't ask me where, but someone modelled this and determined that six blocks was the optimal separation for branching tunnels, specifically for finding diamonds.)
Find Diamonds! You will find diamonds sooner or later. When you do, your work isn't done.
Dig out all blocks surrounding the diamonds first, so that the diamond ore you discovered is floating in space, touching nothing else. This is for two reasons:
You want to know if there's lava directly below them. Nothing is worse than digging out a diamond only to see it fall into the block of lava it was sitting on.
You want to uncover the whole diamond vein: There may be a hidden diamond block whose only connection to the vein you see is at a single corner: By mining out everything, you ensure you have the whole vein.
Once you have your diamonds, immediately run back to base and stash them in a chest. You do NOT want to carry your diamonds around with you.
Once you have some diamonds, the first thing you want to do is make a Diamond Pickaxe so you can mine obsidian (giving you access to the Nether). Then, I recommend making an Enchanting Table (if you have experience to burn), followed by a Diamond Chestplate. Though the chestplate is the most expensive armor to make, it's also the most cost-effective upgrade from iron, and it will help survivability in the Nether more than a Diamond Sword will.
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Amateur dinosaur hunter and extreme weather enthusiast, whose interests include spoken mime, armchair parkour, tactical gaslighting (for fun or for pay), conspicuous ninjutsu and Schröedinger's pentameter—of which this sentence may or may not be an example.
go onto a server, stalk some one, and when they log off, replace the corners of their house with logs (if not logs), make the floor wool, and the cieling glass. Add a sugar cane farm in, with a melon farm too. When they log on, tell them that you will sell the house to them for a diamond.