Instructions
Once you get your Xbox 360 console, the initial setup requires signing on to Xbox Live. The paid Gold membership unlocks online play for all titles, while Silver remains free but doesn't enable online multiplayer. To play Halo 3 gratis from time to time, you need Silver as a minimum, which gives you an online identity, or gamertag.
New Xbox Live users get a free month of Gold membership as a teaser; this is your safest bet for free Halo 3 online, but it's time-limited. Similarly, peripherals and Microsoft Points purchases at stores sometimes come with bonus Gold membership for a limited period.
You'll need to get the Halo 3 game itself, either by purchasing or renting it. Like all other Xbox 360 titles, Halo 3 requires that the disc remain in the console while gaming.
Go to Xbox.com and sign up for your free weekly email update from Microsoft. Any Xbox Live member can get this done easily with their gamertag (Silver members included). Pay close attention to any announcements from Microsoft regarding free online play; these will show up periodically.
Another good place to look is on the Xbox 360's desktop, or NXE (New Xbox Experience). Check sections titled "Inside Xbox" and "Spotlight." These will also feature free online play periods quite prominently.
Make sure to write down the exact times and dates Microsoft offers free Halo 3 game play. Beyond the announced period, only Gold members can join online matches.