Gnar is a very item dependent character. Early game I just kinda play it safe. Doesn't mean no pressure; but usually no ballsy trades. Just poking. Abuse his range and mobility and kiting. Early game mini gnar lacks burst to punish super hard. Mega Gnar lacks dps to kill tanky targets without help of some mini form poke.
You want to focus on CS'ing as well as possible using the wave to your advantage. You get a lot more active once you have some tanky equipment to work with.
IMO his hardest matchups are the bursty AD gap closing fighters that are kinda popular in solo queue. The Wukongs, the Irelias, the Pantheons. Yasuo. Riven is a skill matchup. Armor items generally don't lend themselves to damage or a mid lane powerspike which Gnar kinda needs to be dangerous. I generally just go his health options (frozen mallet or black cleaver (personally prefer mallet), only going for armor if I'm in trouble) If you're in a pickle you could still go Sunfire though. Sunfire is pretty nice for farming side lanes faster.
His easier matchups are AP champions maybe even AP tanks, but AP squishies get crushed by Gnar who waits til he has items in my experience. MR is powerful & MR itemization is very good for him IMO. Banshees Veil can be rushed on him and he still does enough dmg on squishies. I think wits end might be secretly viable for Gnar.
Movement speed is very important on Gnar in general especially on the matchup so don't forget your shoes. I usually go Ninja Tabi if I need to respect an AD champion.
I think it's important to mention that I think overall Battle of Fervor mastery is best for Gnar. Grasp is ok but doesn't offer a ton. Fervor allows you to build even tankier yet have relevant dueling dmg. Getting 2 or 3 BF swords for your autos later game is just OP, and is the difference between being dangerous or a cc bot.
At that I rarely go both Cleaver and Mallet as you lack resistances. Unless I'm buying one for my last slot. I have to choose which one I go (and I choose mallet 85% of the time because peel/pick + more hp). I think if you take fervor you can afford to go tankier items and overall be a stronger Gnar.