Gnar can be quite a versatile champ. He can benefit from a variety of runes and items, from the obvious Conqueror to even Omni-Stone if you're feeling nasty, you can even forego what are commonly considered his "Core Items" like Frozen Mallet and still do fine if you're good with him.
Since all of his abilities offer some sort of crowd control in one of his forms, he can easily keep enemies pinned or slowed down for your teammates to help chase or wail on. The downside is that, like I will touch on in the strengths and weaknesses chapter below, Gnar doesn't really threaten anyone besides tanks, especially late game. While great AoE CC is definitely useful in teamfights, it's likely you won't be doing much damage yourself, and enemies won't be scared to jump you even in your Mega form.
Probably my favorite thing about Gnar is that he may be one of the most underestimated Champions in the game. Since he's apparently earned a bit of a reputation as "the worst Champion" there's a good chance people will underestimate you, which gives you the opportunity to punish them hard. I've found this to be especially true when I was newer and when I first got back into League of Legends, so it could be more applicable to newer players who will be going against other lower level/skilled players. Still, very often I've fought players who thought fighting Gnar meant free kills, they get to play stupidly aggressive, specifically while he's mini because they're always quick to back off when you transform. Funny thing is, the opposite is true in most of Gnar's better match-ups, since he's strong against tanks due to Hyper you usually threaten them more while mini then when you're Mega. I've seen players go so far as to recklessly go in and out of my turret's range to take shots at me, which doesn't turn out great for them.
The two most satisfying things to do as Gnar: First off, when someone will just recklessly enter your turret's range when it will target them, if you're about to transform with your ult ready, you can just toss them into the turret. This is a death sentence for practically every champ if you land Wallop too, cause then they're stunned, taking multiple turret shots, while you wail on them. The second, and my favorite thing to do, is a trick with Gnar's Boomerang Throw. When Gnar's boomerang returns for you to catch it, it will go a lot farther on the return than it does when you throw it. When your enemy is weak and hiding under their turret, probably trying to recall, you just throw the boomerang behind you (away from them) walk in their direction so the boomerang will go that way, then not catch it so it hits and kills them.

Any AP build is by far no end all be all Gnar build. The main reason to use one is if you're bored of the more popular builds, or confident in your abilities. One of the biggest strengths and weaknesses of AP builds is that you might easily stomp enemies when you get ahead but you'll also have trouble catching up if you get behind (in other words, if you're the one that's been getting stomped).
One of the first big benefits I saw using an AP build was that it allowed Gnar to threaten non-tanks. Since Gnar's passive Hyper does bonus damage based on the target's max health, it's a lot more useful against tanky champs like Urgot and Cho'Gath. However Hyper also does bonus damage based on 100% of your Ability Power (same with Gnar's Ult), so while 14% of Maokai's max health could be a lot more damage than 400 AP, the reverse is true against a champ like Ashe where 400 AP is worth more than 14% of her max HP.
Fortunately with the new items for Season 11, there are more options for you to build AP without sacrificing as much bulk. I've found that Gnar's strongest when he has a healthy variety in his build, since his forms benefit from different things. For instance, focusing on damage and defense will make your Mega form a tanky monster, but you're not threatening in Mini form. On the other hand, if you focus purely on attack speed, you'll be shredding through everyone while Mini but almost useless in Mega aside from your CC. This is also why I like the idea of building a more of a mixed AP build, since an AP mythic, Rabadon's Deathcap and one more finished AP item grants you quite a lot of AP, and I prefer that third item to be one that gives you some defense such as Zhonya's Hourglass or Banshee's Veil for example. This gives you room to round out your build with damage, attack speed, and/or more defense.
Before, AP was mostly a fun gimmick build, but now I think it does have some potential in serious play as more of a surprise build. When your team is all AD, the enemy team will likely start stacking armor as early as they can, which will allow you to come in as the surprise AP carry. This might make it a good idea to build some form of Armor pen at some point so you can still deal damage in your Mega form.

While Gnar doesn't have a good reputation in ARAM, it is possible to make him work. I've found the best way to play him in this game mode is to see him as a "set-up" attacker. When you transform, along with when you have your ult, you have the potential to just toss all of your enemies to your teammates, who can unleash on the entire stunned team. It can be especially useful paired with any champs with great AoE abilities, such as Illaoi if she also has her ult.
Gnar isn't particularly good at taking damage from multiple opponents, even while he's Mega unless you've already got some items. This is why he isn't particularly good in ARAM, so unless you are just that ridiculously good with him, in which case you probably don't even need these tips, you're better off keeping your distance early in the game. Very often, when you try to all in when you go Mega, chances are you'll be sacrificing yourself for the greater good, damaging and stunning multiple opponents quickly who then gang up on and kill you, but it will give your teammates an opportunity to kill most if not all of them.