Arighty, here's what you're going to have to do.
First, create an account on bungie.net. You'll need an active email address *Note* Be sure to use the one you entered for your xbox live account. If you don't have one, you'll be prompted to create one. All that is done via this link here. https://accountservices.passport.net/reg.srf?wa=wsignin1.0&rpsnv=10&ct=1207917152&rver=4.5.2130.0&wp=LBI&wreply=http:%2F%2Fwww.bungie.net&id=42917&sl=1&lc=1033
Once you account is created, the gamertag associated with your email address will be recognized. You can edit it if your account if you wish, but if you want to get straight to downloading content, from the home page here https://www.bungie.net/default.aspx, click Bungie Online. From there, you will be given a list of screen shots you can download. If you wish to download something other than screen shots, on that page, there are a bunch of tabs which say "Screenshots, Bungie Favorites, Clips, Maps, Games, Films". Click on the desired category, and download away.
After you've downloaded it (say a clip for example), log onto your xbox live account through your xbox 360, and go to saved film clips. It'll have a star next to it, indicating that it's brand new. Have fun =)