Buy Minecraft from here
Create a Mojang account or sign in if you already have one.
If you created a new account, verify your email.
Fill in your Payment Details. Make sure your on minecraft.net and you're on a secure connection (HTTPS)
Download and Run Minecraft
Open the Minecraft launcher
Log in with your email address if you purchased Minecraft after November 2012, or migrated your username to a Mojang account.
Click on "Play" if you want to play on the newest version.
Enjoy the game.