Hi mate.
I'll try and point you in the right direction.
Just be aware that those that are having trouble are finding it very frustrating, and it's largely persistence that wins the day.
So, I'll assume you have a disc version.
(First job is to make sure all's well and the disc and laser lens cover are clean.)
Anyway, the data you need to remove is on the PS3 menu (XMB)
XMB > Game > Game Data Utlilty folder.
Here you will find a GT6 file.
It contains all the game data and updates you've downloaded so far.
A corrupt file in this data, or the complete lack of a file/s due to packet loss when downloading (particularly when done wirelessly) can cause the install issues. Therefore always use a wired connection if you can, particularly for patch updates.
So to try a fresh re-install, delete this file.
Once that's done, start GT6 offline (don't sign in to PSN) and let the game play.
This will create a new base file in the Game Data Utility folder, replacing the one you just deleted.
While you're in GT6 ...
This is what hall90 was talking about.
In the Start button Options menu in GT6 go to 'Network'.
There you will find a 'Clear System Cache' function.
For the sake of a 10 second task you may as well do it.
Then exit out and quit the game.
Personally, I would then do a couple of Safemode functions to help tidy up the HDD.
http://faq.en.playstation.com/app/answers/detail/a_id/4545/~/ps3-safe-mode-information
Do Options 3 and 4.
Restore File System and Rebuild Database.
That's about as good a footing to begin a fresh download that you can do without reformatting the entire HDD.
So here's where you have a couple of options.
You can either load GT6 and start patch updates from there when it automatically prompts, or you can do it from the XMB without actually starting GT6.
XMB > Game > GT6 game icon (press triangle) 'Check for Updates'.
Either way you will be taken to the update screen.
Here's where the 'step by step' business starts.
Each file (patch) will download and then install one by one.
Once installed, the next patch will begin downloading and then install, etc etc.
It is possible to cancel out of the download once a file has installed. (circle button)
So if it says 'Downloading File 1 of 9' allow for the download and install process of that file to finish.
When it changes and says 'Downloading File 2 of 9' cancel the process.
You now have updated to the next version ... eg v1.01.
So you should now be able to play the game (by cancelling the option to Update Software when you start the game) and check everything is okay.
By repeating this process you can update a patch at a time, instead of hitting it with one huge lump.
On a side note, just be aware of this known issue for updates after v1.02.
Not sure if it will affect you, but here's what to do if it does.
http://www.gran-turismo.com/au/news/00_3266694.html
Other info.
v1.01 and v1.02 were quite large. (over 1GB each)
V1.03 - v1.06 were all quite small.
Then v1.07 and up are again at least 1GB.
So you might want to skip through a few of the patch download steps when you see a run of small files downloading.
It's not a magic bullet.
So don't look at it as a guaranteed fix.
But I hope that explains a few of the things you've read in this thread.