You'll find the Road GT Series event in the Career section of the main menu.
The event consists of 7 weekends and each weekend consists of one qualification round (which allows you 2 laps to better your starting position on the grid), followed by two 5 lap races. To complete the series with maximum points you'll need to win all 14 races.
To make this as easy as possible on yourself I suggest you first of all go to Options from the main menu and set the difficulty to Beginner as well as turning Damage to Off.
Then when you go to Road GT after entering Career you'll be shown a list of cars you may choose from to use on the righthand side of the screen. I chose the F512 M as I found it handled pretty well overall, but it's up to you which one you go with. I tried the 458 Italia first but I found I couldn't get out of last place on the very first qualification round - I was 4 seconds off the pace after multiple attempts. I switched to the F512 M and had no problems.
Once you've picked your car you'll be asked to choose a setup. I suggest you go with Arcade since Assisted will brake too much, resulting in slower lap times, and Simulation will be very difficult to control.
You'll then be asked to choose Assists. I recommend Automatic transmission and also to set SC Strength, TC Strength and ABS Strength to Max. Racing Line is up to you but I turned it on as I found qualifying to be much easier knowing when exactly to brake.
Now let's get started!
You should ALWAYS choose to do the qualification round, as starting 1st on the grid makes winning the races a piece of cake.
IMPORTANT: Now, this mode does NOT have a retry option so you're going to want to quit to the XMB via the PS button if you didn't qualify in 1st place, or if you're not going to win a race. Doing this will restart you at the beginning of the qualification round or race that you were just on. Just make sure to do this before continuing.
It's not crucial that you qualify in 1st place, but to make things as easy as I could on myself I didn't settle for anything less than at least 2nd place, and I recommend you do the same.
The second race of each weekend starts you in the position that you finished the previous race in. So, as for the sake of this trophy you MUST finish 1st, you'll always start in 1st for the second race.
All up, this trophy will probably take you about 3 hours, give or take, but follow my recommendations and you should have no problems with it!