The simplest way to play Xbox 360 games is to insert the disc and start playing. However by installing a game to the hard drive you can significantly improve in-game loading times, and can also prevent slight pauses mid game play. It achieves this improvement by virtue of the fact that data rates are faster when reading from a hard drive then from a disk, thus speeding up the in-game loading. All games can be installed to the hard drive, however your performance may vary from game to game.
Sample Install Screen
Notes:
- You still require a disk to play the game, since it checks for the copy protection which is present on the disc.
- You need an Xbox 360 with a Hard drive of at least 20Gb attached as each game may take upwards of 7Gb of disc space
Steps
- Ensure the disc for the game which you want to install is in the Xbox Disc Drive and navigate to the “My Xbox” blade on the Xbox dashboard. If the game automatically starts, or you are otherwise not on the dashboard, press the xbox button on your controller and press “Y” to return to the dashboard.
- Navigate to the “Game Library” box and select the game you wish to install (Must be the disc in the drive).
- Select “Install Game”. This process will take approx 5-15 minutes depending on the game. A progress bar is shows the percentage completion as it runs. Exiting this screen during the installation will cancel the process.
- Once the progress reaches 100% press “A” to leave the screen. You can now play your game and use your Xbox as normal.
Happy Gaming 
Image via MaddenMinds