Update: The demo should now be available!
The nice thing about making a racing game like Gran Turismo 6 for current gen consoles rather than next gen is that those consoles are already out there. Thus, you can do things like release a demo. Lucky us, Polyphony Digital is doing just that and we can expect a Gran Turismo 6 demo to be released on July 2 just as the real-life racing GT Academy gets started.
Not so coincidentally the demo will include a few tutorial levels based around the GT Academy training camp, followed by the Silverstone Grand Prix Circuit itself. It's all on just a single track (who knows how big of a download just that will be). Top qualifying times from the demo will qualify players for their own spot in the real GT Academy, a racing league that's ridiculously legit considering it's been spawned from a video game.
In a contradictory statement, PlayStation EU is saying the demo will go offline starting August 31, but the North American PlayStation Blog says the demo will remain. Either way, check out the PlayStation Network shop starting July 2 and try out the Gran Turismo 6 demo on PlayStation 3. Who knows, you may find yourself racing the real thing afterwards.