Read this in a 50's infomercial style.
With your new Xbox 360, you can do multitudes of new, and exciting things!
For example, with your purchase of Xbox Gold Online Membership, you now have the opportunity of making a "gamertag" and playing with other people online. Your gamertag is your alias on Xbox Live, Microsoft's online gaming network. You also have the option of adding other people's gamertags for easier contact and the ability to play online video games with them regularly.
The initial setup of a gamertag is fairly simple, and some relatively reliable information on the subject can be found here: Link
Try to ignore the multitudes of exclamation points so that your eyes don't fall out.
My gamertag's the same as my username on this site in case you want to add me to your friends list.