Trundle is a tanky fighter who specialises in sustained fighting and artificial value from his abilities. He buffs himself while debuffing the enemy, allowing him to remove tanks from a fight and simply out stat many 2 v 1 scenarios. He's very sticky, yet has several tools to disengage. I often take him as a first pick, against champions I don't know a counter for, or against tanks who need to be stopped in lane/to garner the attention of the enemy jungler. Why? Because he has by far one of the most flexible builds in the whole game. He can function as a fairly lightweight fighter by sapping tank stats from unwilling lane opponents, or as a mega tank who grinds down enemy carries.

Personally, I believe he's at his peak against AD fighters who will build armour and health relatively early IE Garen, Jarvan etc. While having a simple kit, he's all about paying attention to cooldowns and seizing opportunities to punish his opponent. This guide will start with a brief description of Trundle's role in the game depending on whether he's a fighter or a tank.

Early game Trundle is very good at beating champions with high cooldowns and low mobility. His Q is on a low cooldown of 4 seconds and only costs 30 mana, making it relatively easy to scoop up extra CS for little cost. Now, there are three ways I play Trundle early game: Shrek, Donkey and Prince Charming.
Shrek, you play very aggressively because you simply out damage. You go for Q's if they get close and once you're certain you'll get kill or a flash, pop a pillar up behind them as they go into CS. Throw your W as far down the lane as you can and proceed to start bonking them. It's a simple strategy, but an effective one. The most extreme example of this is against Nasus. Every wither you force out of him is 4 less stacks.
Next is Donkey. You talk **** from a distance but don't want to fight them yet. This is the grasp of the undying style where you only want quick brief trades to eventually push them out of lane. This is mainly for Juggernauts and champions that win sustained fights harder than you IE Illaoi.
Finally, Prince Charming. Play like a lil ***** and CS under turret. Most ranged champions are taken on with this style until an opportunity presents itself. Let's say Kayle has pushed you under the Blue side tier 1. If her E ends and she's near a wall, use that chance to give her a schneaky pillar and whack them a bit. Even if you don't get a kill, the Kayle player will probably be a bit spooked.

If you're consistently pushing your opponent under turret with Tiamat or forcing them to back, feel free to roam. Your ganks are surprisingly potent due to your E being so powerful.

Mid game Trundle shines at splitpushing or functioning as bodyguard with semi engage in teamfights. Duelist Trundle tends to be better at the former, while tank Trundle is better at the latter.
Split pushing with Trundle is basically a beacon shouting "Come get me u lil *****". Either at least one person will toddle up to lane to be murdered, or you'll waste their time due to how difficult you can be to kill mid game.
Mid-game teamfights, you have three jobs you need to balance: Semi engage, Peel, and partying with their backline. Well I say partying, it's more like... clubbing. Against heavy mobility comps, you should focus on semi engage and peel, since you'll probably just get kited while they reduce your ADC to goop.
If you're confident your carries will be safe or that you're doing the carrying, you can also look for flanks. Flanks are powerful on Trundle since he can place his pillar in an awkward position more easily. If you can catch out one or two champions that have overextended, you can isolate them fairly easily.

Late game Trundle is more heavily confined to peel and engage. Your main job is to set up your team to kill the tanks before or after they engage on your team giving you a chance to siege or to simply walk in and **** up the place.

Late game Duelist Trundle is still able to duel Tanks and Bruisers. However, by this point a lot of Immobile Carries are powerful enough to wipe him out. Tanky Trundle however can take their burst and beat their little booties if they're on their lonesome and can't kite you. ADC's become your worst nightmare though. If they have a high dps such as Jinx or Vayne, stay away and only try to fight them if someone's around to burst them. If they have that reload mechanic IE Graves and Jhin, you still stand a chance. While it's optimal to ult tanks, you can still ult carries if you want them dead a bit faster.

Alrighty, so most of you folks out there are going down the resolve tree and taking grasp of the undying as your keystone. This is alrighty if you plan on building very meaty with a lot of HP, but there's a small problem with that. You probably aren't. Unless you're getting very fed in lane, at most you'll have two items, the most common first item being a Ravenous Hydra, followed by a mainly resistance item. Again, this is fine if you're taking lots of quick trades, but honestly, I think Fervor is significantly stronger by level 6 - mid game, and allows you to offer some decent damage late even when tanky.

The reason I believe it's a lot stronger on Trundle now isn't just due to the stickiness, but due to the tweaks to fervor that cause you to gain flat AD rather than simply bonus damage. This is very strong on Trundle since this also increases the damage on your Q which maintains the stacks as it's an AA modifier. During an extended fight (which Trundle will almost always be in) Fervor will almost always out damage grasp.

This is an interesting topic for Trundle players. The thing is that whilst I support taking Fervor for bonus AD, I dislike the view of Ravenous Hydra as a core item since I feel that in the long run it does less damage than Titanic. Trundle will Normally have at least around 3000 HP. With a 40 + 2.5% hp damage bonus, this will do around 115 extra damage. Ravenous Hydra provides 75 AD, with 15 bonus damage to Trundle's Q. 115>90.
Ravenous however does more damage sooner and allows him to take towers sooner whilst being a stronger dueliest. Trundle late game can be hard to kill, but he can also be kited to hell and back, so Ravenous to splitpush mid game so this is never a problem is understandable. However, TH gives him a far greater presence in teamfights as a tank as well as allowing splitpushing, thus I personally feel it's the stronger variant on Trundle unless snowballing.
However, if you want to build TH in a game, I strongly recommend holding off completing it until your 3-5th item. The passive won't be very effective early game and there's better items available for you.