Only go deep enough to find a few stacks of cobblestone, at least half a stack of coal, and 8 iron ore.


Use the iron to make 2 buckets and a pair of shears.
Have at least one 9x9 plot for food. (If you're short on flat building space, you can line the top of your house with dirt.)
Have at least two 9x9 plots for trees. Birch is best, as it is the easiest to harvest quickly. You can easily fit 25 birch trees in a 19x19 (four 9x9 plots without interior fences) plot.
Plant a torch next to each tree so they will grow at night. If you have the time and the cobblestone to spare, consider making the entire plot cobblestone except for where you'll plant the trees. This will make replanting easier.
Make at least one, but preferably three, 9x9 plots for sheep. Dye your sheep 3 different colors. Red, green, and yellow are fairly basic choices, as they're intuitive, easily visible, and the dyes are easy to acquire. Now you're ready to start financing your expedition.;
, Shear your sheep, then cut your trees. Shear your sheep again. Collect your saplings and replant your trees. Shear your sheep. Harvest and replant your food. Rinse. Repeat.
 It's best to carve yourself a 3 meter (9.8 ft) wide road from your home to your mine with slabs or steps so you don't have to jump or fall when travelling--jumping increases hunger. One torch every 10 meters (32.8 ft) is sufficient to keep monsters from spawning on your road.
 Be sure to include a double chest for loot, a bed, a crafting table, a furnace, and a 2x2 pit for an infinite water source. Put a door to the mine and a door to the world. Build a small (3x6 meter is enough) fenced-in area in front of your door. This will allow you to kill any monsters you find hanging out when you come out of your mine. Now put pressure plates on the safe sides of your doors and fence gate. This way the door automatically closes behind you. Make sure to light the outside of your shelter so no monsters spawn in your safe zone.
 Gather resources again.


You need to leave home with:

2 stone pickaxes, 1 stone sword, 2 stone shovels, and 1 stone axe
1 stack of food, 1/4 stack of seed, 2 buckets of water, and 2 stacks of dirt
1 stack of torches, 1/2 stack of cobblestone, 1 stack of each color wool, 1 stack of logs, 1 stack of sticks, 1 stack of planks, and 1 crafting table.


Don't bother with leather armor; it takes more time than it's worth.
 Immediately walk a reasonable distance, throwing torches down blindly while you kill monsters. Return to your door. As you're killing monsters, try to locate all directions they can come from. Block them all off with dirt. Now that you're in a big room by yourself, you have time to think and plan. Light this room enough that no monsters can spawn.
 Throw three of them down in the middle of the room in an arrow pattern, pointing to your door, then put a torch right next to them. Double-check each wall of dirt to make sure no monsters can get into your room. Don't forget to look up, as monsters can survive a fall of a few meters. Put a block of red wool in or near each wall blocking unexplored areas. Block off any sources of running water or lava. Dump water from your bucket near (not on) any standing pools of deadly lava to turn it into less-deadly obsidian. Now mine this room of any valuable ores. Build stairs and paths to any inaccessible areas. Optional: clean up the room so it's not a disgusting mess; you're not a child. Now, pick a direction to continue. Dig out a 1x2 entrance to the next space. Repeat step 1. Place a yellow arrow pointing home every time there's a fork in the road. Collect the dirt walls, and the red wool, that you no longer need.
 One coal smelts 8 ores, so do this every time you get 8 or 16 iron ore.  The first item you'll need to craft is an iron pickaxe, to mine ores that you can't mine with a stone pickaxe. (Later you may choose to use iron tools entirely, but for now only use it when you have to.) The next item is an iron sword. Then start making armor. You'll have a full kit before you know it.
 Mine a few blocks extra just to be sure there's nothing hiding behind it, then turn around. When you come back to a fork, place a block of green wool at the entrance to your cleared tunnel so you know not to bother going that way again. Start off in a new direction.
 It's probably best to only return to your shelter when your inventory starts to fill up. When you do return to your shelter, first replace your broken tools. Next, replenish your stock of torches. Finally, drop your extra loot in your chest. If night has fallen, sleep in your bed at least once so that if you die you'll respawn in your shelter instead of back home.
 Continue doing this until you're two or three safe rooms deep into your mine. Here you'll want to start a mini-farm to replenish your food supplies. You may want to plant a couple of trees, but you'll most likely run out of wool before wood becomes a problem.
 Remember never to go home without taking a full load of loot back with you. Congratulations, your Steve has learned a trade.
Don't try to explore deeply before you have a good home base set up near the soon-to-be-mine.
Spend a few game days preparing.
Go select a good cave to start mining once you have enough materials.
Build a shelter of cobblestone completely covering the entrance to your mine.
Return home.
Enter your mine.
Craft a few yellow (or your choice) carpets.
As soon as you collect 8 iron ore and some coal, go back to your shelter and smelt it.
If you come to the end of a tunnel, congratulations.
When you break your tools, you can drop your crafting table and make some more on the fly (make sure to pick it back up), or you can return to your shelter.
When you've gone deep enough in your mine that returning to your shelter is inconvenient, just build another one complete with crafting table, bed, water source, and all.
When you start to run low on wood or wool, you'll be returning home.
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