How do I get an XBox 360 to update games?

Solution 1:

When you log into Xbox Live and then load a game, you'll be automatically prompted to download updates to the game, if they are available. If you refuse, you'll be signed out of Xbox Live for the session.

Note that most Valve games that got special PC updates don't get those updates on the Xbox 360 - I'm pretty sure that the "potato sack" and/or "Portal 2 ARG" updates weren't released for the Xbox 360. Also, almost all the TF2 content that Valve's released to-date is unavailable on the Orange Box for Xbox 360. Just to kick you while you're down, you have to pay money for the L4D/L4D2 expansion packs on Xbox 360, where they're free on PC.