I explore caves until I've conquered all the ones reasonably close to home, then I start clearing out and harvesting everything from level 16 downwards, including the lava (obsidian).
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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."
I mine in several ways. Typically, just through cave explorations. Sometimes, I'll cut out a 30x30 room and just start digging down until I have a really large hole to bedrock. Then, I just drop excess cobble into my incinerator (which is just an exposed lava source on the surface that I blocked off with cobble except for the opening to throw stuff.
I usually strip mine, since its the most efficient, however, I keep 3 blocks in between each strip, since most, if not all, ores are found in pockets that are 2 blocks wide or larger. If I have a lot of time on my hands, I repeat this in all 4 directions anywhere from level 6 - 24.
dig out a 9x9
dig a tunnel out in a straight line
then go back and clear the left and right sides every third block
When my main branch hits 200 I dig a 12 by 12 then branch again
Chest go in the rooms to hold blocks and items so nothing goes to waste.
Along with a furnace and table
A mineshaft straight downtown level 12. Ladders and torches all the way down. A landing every 3 block drop. At level 12, 4 main tunnels 100 to 200 blocks long. Side tunnels and then branch tunnels connecting the side tunnels.