I had no idea that getting the DLC was so confusing for some people.
It seems like a bit of a no-brainer to visit the PS Store......
Well... yes and no. Go to the PS Store and buy the DLC, sure - easy-peezy. But then you get the download screen, and you get to download a GT Academy theme and a Stealth NSX (if you're in North America, anyway). But no DLC is found there to download.
You've been charged for it, but it doesn't appear in your download list, or in your cart, or anywhere else, except in your transaction history, which shows that you've been charged for it.
So you go open up GT5, click the download button, and there's nothing there either. So you quit the game, try looking in your Account Management area on the XMB, find no help there, go back to open up the game, and still nothing, and repeat - and then after a half hour or an hour, the DLC magically shows up in the download area of your game.
Yeah, I don't know why that would confuse anyone...
This is the only time I've ever downloaded anything from the PS Store where it worked like this. I have to say I'm quite unimpressed with PD's integration of DLC.