Instructions
Using Xbox 360 Console
Turn on your Xbox 360 console and allow it to display the main menu.
Scroll to the "Sign In" option, located within the "My Xbox" tab.
Press the "A" button to view your Gamertag, which is composed of the username and avatar you had selected during the profile creation process.
From Xbox Official Website
Navigate to the Xbox Live homepage at www.Xbox.com/live and click the "Sign In" link from the upper right section of the screen.
Type in the Windows Live credentials associated with your Xbox 360 account, such as your Hotmail or Windows Live Messenger information. Click "Sign In" to proceed.
Note the Gamertag username shown in the upper right corner, which also displays the avatar initially chosen during the profile creation process.