First off you don't actually need to have competed Grounded Mode normal to unlock plus mode, you can complete the game in your first playthrough on any difficulty (e.g. easy/normal) then you can unlock this mode with the following guide;
http://www.playstationtrophies.org/forum/the-last-of-us/2436...This will give you all the difficulty trophies for both new game + and normal mode.
For the actual play-through you could either just play through using basic trial and error, or take advantage of a few exploits in the game, the first;
Unlimited Shivs- Very useful for killing clickers and opening shivs doors, which could give you more ammo/supplies/medkits;
Using photo mode- As listening mode is disabled for this difficulty, you can set up photo mode up so that when you press L3, you enter a mobile 3rd person perspective, allowing you to see any enemies around you better.
Finally make sure you upgrade all of your weapons and meds for the 'boss' fights, makes for a much easier time, but don't forget, you will die, a lot, so don't get too disheartened.
There is also a brilliant guide by PS4Trophies on YouTube for Grounded mode as well-