First Night

Your first night is going to be the toughest. You don't know whats happening out side of your little indent, you call home. There are Spiders, Creepers, Skeletons, Zombies with only one mission, to kill you. First off they can't open doors. First you are going to have to craft a sword.

Swords can be crafted out of wood, stone, gold, steel and diamond. It would be a good idea to keep one of these inside your inventory at all times. That is if you don't want to be be killed and lose all your stuff.
After you make you sword you can make a furnace out of stone like such.

After you make you furnace you should expand your cave to accommodate all your stuff. A size like this shall do.

You should also create a storage box you can create one by crafting it with the crafting table like such.

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Going out side at night time can be extremely dangerous. Be careful make sure you have torches and a sword handy. You will need it unless you are playing on peaceful. Then you wont need to make a sword to fight off enemies, only reason being is that there will be no enemies.
Once out side and playing on any difficulty except peaceful the odds are you will find some mobs. You can find a mob list under the "Mob List" page.

Here is a common enemy, and probably the most annoying, the creeper.

The creeper will produce a hissing sound then finally explode. The crater it will leave is pretty big here is an example.

There you have it, if it starts turning day, congratulations you made it through your first night in Minecraft.

~MCF