Insert a game disc into your console's disc drive. The game will automatically install on PlayStation consoles. On Xbox consoles, you'll be prompted to install the game. Please note: Call of Duty: Modern Warfare II requires a Day One update in order to play the game.
Yes, Call of Duty: Modern Warfare 3 has full cross-platform support. This means that you can squad up with players on any console  PlayStation, Xbox, or PC  and enter the battlefield together. This is true for any online mode in the game.