This article explains how to transfer your data from an old Xbox 360 to a new one. You will need a special transfer cable from Microsoft. You will need to buy the transfer cable separately, but they are not expensive.
Data Transfers on Xbox 360 – IGN Tech Tip of the Week
Before you begin a transfer, you should update your Xbox 360 software if it is not up to date. To do this, connect to the Xbox network via an internet connection.
Select the Guide button on the controller.
Go to Settings and then to System Settings.