Getting Started With Minecraft

1: Get the game

You need to be online to download the game, but not to play it.
Head over to www.minecraft.net and register an account. You can now either purchase the game, or download it to try before you buy.
Don't buy the game anywhere else; due to the popularity of MInecraft it has attracted numerous scammers and copycats.
Launch the game; it will ask you to log in. If you have not paid, you will only be able to play in a limited demo mode, but that's more than enough to get a feel for the game.

Online vs offline play: Player information, such as achievements, is stored online, but everything else about your world is stored on your computer. This means you can play the single-player game just fine without an internet connection. Achievements will behave a bit strangely, but that is all!

2: Your First World

Press the Single Player button to start your first world. You will see a list of your saved games, which will be empty at this time.

Press Create New World.

You will be asked to provide a name for the world (this can be changed later if you don't like it) and choose a game mode.

Game Modes

Survival

This is the "normal version" of the game. You will need to fight off monsters and find food to survive, and find or farm resources to craft items and build things. There are multiple difficulties you can choose from. If you die, you respawn and carry on.

Creative

This mode is purely for building things. Monsters won't attack you, and you have access to all the resources you could want.

Hardcore

This challenging mode is for experienced players only. You only have one life; if you die, that's it and everything you have built is lost.
There's a button saying More Options which we can ignore for now. Press Create New World and the computer will generate your first world and place you in it.

3: Take A Look Around

You should see something like this:

Grass, trees, maybe some water or animals. Or you might be in a desert, or a snowy mountain. In any case, it is early morning and you have a whole day ahead of you. At night time, monsters will come out and you will want to have prepared a shelter of some kind by then.
A day in Minecraft lasts 10 minutes.
Check out the controls you'll need to move around and do stuff.
What's all that stuff on the screen?

4: Survive your first night

Assuming you're in Survival mode, you have 10 minutes to get ready for nightfall. Otherwise, monsters will kill you.

You can download the minecraft mod 1.7.10 here:  http://www.crazyminecraft.net/