How do I quickly create a safe shelter?

If you're willing to carry a door on you, the quickest shelter you can throw up is to just dig a 1x2 hole into the side of any hill and throw down a door to seal it off.

If you don't have a door I suggest the following:

  ▓▓▓ ▓▓▓
    ▓▒▓   top down view 
    ▓▒▓   
    ▓▒▓▓  ▓ 2 rocks
    ▓▒•▓  ▒ 1 rock
    ▓▓▓▓  •   you

The key thing here is that by being off to the side you aren't in range of arrows, but you still maintain a path to light so you can see the sun up (you can also listen for music, but I often disable sound). You close off the entrance with single rocks so you leave a 1x1 path which zombies can't come down.

The big trick here is wooden blocks, and some coal for the lights. Each log block you get from a tree will give you 4 wooden blocks, which you can use to build a seperation and a door.

Now, here is a step-by-step tutorial, assuming a completely new spawn.

The First Day

• Punch down a single tree, this'll give you usually 4-5 logs. (you'll need at least 4)
• Find a place with some coal.
• Turn all logs into wood.
• Create a workbench
• Turn 4 wood into sticks.
• Make a wooden pickaxe.
• Mine 3 cobblestone.
• Create stone pickaxe, use that one from now on.
• Mine at least 8 more cobblestone and all the coal.
• Create a stone woodcutters axe.
• Cut down at least 4-5 more trees.
• Turn all logs into wood.
• Create a door.

You should now have enough wood to create a safe shelter for the first night, with a nice door allowing you to look outside and see when the morning has started.

Ensure your hideout is at least 5x5 on the inside, to protect you against creepers when you stand in the center.

You are now ready to prepare yourself during the night for the second day.

The First Night

• Stay in the center, or at the back wall this will ensure you that creepers won't be able to get close enough to explode.
• Create a stone sword, and a box to store your stuff in.
• Store your stuff in the box, only take the stone sword.

The Second Day

• Wait until the zombies and skeletons have burned to death.
• Run outside for about 10 blocks, leaving those mobs that stand near the front door behind you.
• Secure your surroundings using the sword we made in the night. (use hit and run tactics when needed)
• Stash your rewards when it is safe to do so.

Now, the only mob you need to be afraid of, is the creeper, which explodes when he is near you. If you hear the telltale creeper fuse sound, make distance between you and the creeper. Killing the creeper is the easiest when using hit-and-run tactics.

Just a note on the spider, while big and annoying and still dangerous, it is far less less dangerous compared to the creeper.

Honestly for my first night in a new game, just dig six blocks into dirt, and wall off the entrance.

I almost never stay in that first shelter, so it's really just to keep me alive until dawn, after that you keep hunting for a good starting place (near a cave, trees, etc.) then you build there. Heck even if I'm established in a world and I'm just exploring, i'll dig a dirt hole to hide in for the night (Though if I'm established I'll carry some glass so I can see out). Worst case scenario is that you get a creeper stuck outside, in which case you dig the other direction until you're back outside.