You just spawned in. NO TIME TO WAIT AROUND! Grab that axe and start chopping! Get about 25 timber, then put 20 on the ground to chop into wood. With that wood, press C to open the crafting menu, then make a workbench and 20 sticks. Don't place the workbench yet. Go around and frantically right-click the rocks lying around until you get ten of them. When you do, find a ladder that leads underground and place your workbench right near it. Now it's time for crafting.

Now that you have a workbench and the optimal materials, make a Stone Pickaxe and Stone Furnace. Place the Stone Furnace and make Coal with the rest of your Timber and some Sticks as fuel. When that is done, turn all the coal into Torches, and you'll be able to descend into the caves you put your things near.

Now you're underground. Hold your torches so you can see around you. With your sight enabled, evaluate which environment you are in:
There's nothing around but stone. No ore, no caves, nothing. If you're in that situation, you need to pack up and move to a different ladder.
There's some other stuff in your box that isn't plain stone. Here are the possibilities and what you should do:

• Black Pieces = Coal. Ignore it, you can find more later if you find a cave.
  
• Brown Spikes = Sulfur. This is a late game thing, leave it be.
  
• Orange Ore = Copper. A decent find, but only worth it if it's a really big cache. (16 or more)
  
• White Ore = Iron. Perfect find! Grab any and all iron in your box, it's the key to survival.

When you mine whatever is in your box, leave the area and find a new ladder.
If you start inside, next to, or close enough to a cave, you're in good luck! Place torches around until you run out. While you're looking around and putting torches down, you might find these:

• Black Pieces = Coal. Gives you more torches, mine it if you're low.
  
• Brown Spikes = Sulfur. This is a late game thing, leave it be.
  
• Orange Ore = Copper. Good ore if you aren't able to find any Iron.
  
• White Ore = Iron. Perfect find! Mine all the iron you can find, urgently.
  
• Spiders. Ew ew ew ew ew ew ew ew ew ew ew ew ew. Good for making bows.
  
• Zombies. Not very special, but they chase you as fast as you can run.
  
• Skeletons. AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
  
• Random Wooden Wall. Basically a giant spider nest. Wait until you get a sword.

Now that you've scouted out your cave, ask the question: Did you find any iron?

You're going to have to look further! Look for coal in the mines to make more torches. If you run out of sticks, make more, and hope it's still day if you run out of wood. (You can check the time in your inventory)
Repeat this process until you find iron, then continue to the "Yes, I did" part of this guide.

CONGRATULATIONS! You found the key to surviving! But, you need to ration out your iron carefully. Here is a list of what you can use your iron for, and how important they are (scale of 1 to 9)

• Iron Sword - 2 Iron, 1 Stick - 9 Importance
  
• Iron Pickaxe - 3 Iron, 2 Sticks - 8 Importance
  
• Iron Breastplate - 8 Iron - 6 Importance
  
• Iron Leggings - 7 Iron - 5 Importance
  
• Iron Helmet - 5 Iron - 4 Importance
  
• Other Iron Tools - 1-3 Iron, 2 Sticks - 5 Importance
  
• Iron Bow - 5 Iron, 1 String - 3 Importance
  
• Iron Arrow - 2 Iron - 2 Importance
  
• Bursting Arrow - 1 Iron Arrow, 1 Gunpowder - 1 Importance
  
• Bucket - 3 Iron - 4 Importance

Usually, you can find a LOT of iron in one cave system, since they seem to go on forever. When you get most or all of these items, you've basically won. Make sure to equip the sword in your second hand. Copper can be a good replacement for iron in most of these recipes, but it's worse than iron.