To download Minecraft, visit Minecraft.net and click the link with the text Download It Here. The Minecraft download is available for Windows, Mac OSX and Linux.
You can download Minecraft for free, but you must purchase an account to actually run the game. As of 2015 a Minecraft account costs about $27. To install Minecraft on your computer, double-click on your downloaded file. The software prompts you to log in with your username and password.
Upon the first installation of Minecraft, the game client automatically downloads any additional game files or updates. Minecraft was built in Java, so you must install Java on any computer on which you wish to run Minecraft.