Tutorials/Your first ten minutes
This is not a game guide, so if you're looking for definitions, you've come to the wrong place.
You spawn in a world with water, sun, trees, animals and hills.
 Minute Zero
Look around, take note of your surroundings. See if there are any trees around you.
Walk towards trees. Throughout the first day, it's recommended to hit any Tall Grass you come across as wheat seeds are going to come in handy later on.
 Minute One
Punch down the trees in the surrounding area. Get at least four logs.
 Minute Two
Make a Crafting Table (1 log = 4 planks)
Make wooden pickaxe (1 log = 4 planks = 8 sticks)
 Minute Three
Dig down or into hills, and use the pickaxe to gather 6 blocks of cobblestones. This hole can be your shelter if you want, so pick a suitable place.
It never hurts to get more wood, so try to have at least 10 logs for the night. It's okay if you don't get enough. You can collect more in the morning.
 Minute Four
Wander around and look for coal and a place to make your shelter. Usually on the walls of cliffs. It's okay if you can't find coal, just cut down some more wood and turn it into charcoal later.
You live in the world.
 Minute Five
Chop up your Crafting Table and collect it and remember your spawn point.
Walk around, looking for an ideal place for your shelter. If you see sheep, kill 3 of them to gather 3 blocks of wool. If you want to have an easier time later on by breeding sheep, don't kill sheep unless there are 5 or more around.
 Minute Six
Clear the area for your new shelter. You can make an easy shelter by digging into a hill or digging steps downwards into the ground.
 Minute Seven & Eight
Build your basic shelter (worry about size and looks later, focus on functionality).
Craft some torches to light your shelter up.
If you have additional wood, make a door.
 Minute Nine
Get ready for the night and craft a bed if you gathered wool. Note that the color of the wool doesn't matter; you can use any color of wool you have (and any combination of wood you have.) This, however, does not affect the output's colors.
 Minute Ten
If you don't have enough wool then what you need to do is start to make a mine. From mines you can get lots of useful items such as iron, coal, redstone, gold, lapis, diamond, and emerald. You should start to mine in a staircase pattern (so you can get back up.) Mines are also a good way to find caves.
If you don't have enough coal to make many torches for the mine you can make organize your items and house to make finding and moving easier.
If you decide to start making a mine, there are many methods to dig for resources. While a safe method would be simply to dig a large room, lighting it up as you dig while looking for ores, a more profitable decision would be to look for a cave and start spelunking. If you decide to find and explore caves, a sword, food, and a light source (presumably torches) are absolute necessities. If you come across any ore other than coal, stone, or dirt get a stone pickaxe before you mine it, as using an inferior pickaxe will not only take longer to mine it, it will break the ore without dropping the resource. Be prepared for hostile mobs, as it is a common but fatal mistake for starters to think that the moon spawns hostile mobs, and not simply darkness. If you come back with enough iron, you will be able to experience many more features of Minecraft, mainly redstone, pistons, diamond, and much more. You have started on your path to your success in Minecraft, whether you found iron or not.
 Other options
One good idea is to chop extra wood and burn it for charcoal. With practice, you can start a new game and as long as you are near trees when you spawn, you should be able to make basic tools, a furnace and have enough wood for torches before midday (5 minutes).
Often people would rather use up wooden tools before switching to their newly made stone tools, but the stone tools really are better -- if you don't want to "waste" the wooden tools, you can use them as fuel to smelt single items.
If possible, and if you can spot a position where you would like to build your house when you spawn, try to gather the resources from nearby, and only dig where you would otherwise dig to construct your house to save time later. Replant all saplings as soon as they fall if this is the case so that you have less distance to walk later.
Remember, dig tight and don't let the Zombies bite.