At the moment, Trundle is best in lane rather than the jungle, because he is a strong counter to many currently popular top laners. during lane phase, you want to do two things: Farm aggressively (try to get as many last hits as you possibly can, even at the risk of taking some harass) and take frequent trades with opponents (if you don't have a minion to last hit, look for an opportunity to land an AA>Q two hit combo on your lane opponent for a good chunk of damage). The only reason you can do this is because you have arguably some of the best built in sustain in the whole game. Every time an enemy unit dies, your passive heals you (as you undoubtedly know), meaning you can afford to take a bit of harass when last hitting where most champs would suffer a lot more for it. the same goes for taking otherwise unfavorable trades, since you can heal it all up very quickly leaving you with a health advantage over your opponent.
Pre level 6, you do not want to try and kill your opponent in lane unless you get a jungle gank or they are stupid and standing right next to you at very low health. Going out of your way to get a kill early game only serves to make you miss CS and put yourself at major risk of being ganked or simply getting killed outright. Once you hit 6, your kill pressure in lane becomes quite immense. If you and your opponent haven't backed yet, you should be much healthier than them, and if you have both backed, your CS advantage should mean you have better items. Try to harass them consistently and then go for an all in when they are vulnerable (i.e. if they have a mobility ability, bait it out first, if they have flash, ghost, heal, etc. do the same, try to fight them starting as far away from their tower as possible) To begin with, place your pillar behind them somewhere that they have to walk far around it (ideally next to a wall so they get stuck behind it) then drop your W ahead of the area they will run to and start beating on them with AAs and Qs, and pop your ult before they get under tower range so you get extra tanky and they become squishier for you to kill more quickly. If you have ignite, use it now to help secure the kill. At this point, if you did it right, they should be dead, you'll be at about half HP, and should be able to sustain off the minions and then take their tower.
As for build, I really like starting BotRK most of the time, since it is great for early dives like your level 6 all-in, and generally offers a lot of what trundle wants. after that, go for a sheen item (Trinity force if your ahead, Iceborn if your team needs you to tank up quick) because sheen items help you get off better burst trades with AA>Q combos. After that, getting a Spirit Visage is excellent and really works great with your passive, your BotRK lifesteal, your ult, and your W. Dead man's plate is a great pickup after that, since it helps you stick to enemies while keeping you durable, and to round out your items I like to get a titanic hydra since it allows you to deal a huge amount of damage while being very very durable. Boots are something you should choose based on the situation and build whenever you feel you need them. Trundle as a champion is able to use all except for Sorc shoes very well. Ninja Tabi make him much more durable, Merc treads help him in CC heavy team fights, Swifties help him stick to enemies really well and run away effectively, Lucidity boots allow you to spam Q and have pillar on an incredibly short cooldown, and mobi boots help you roam and split push really well.
Late game I usually prefer to use Trundle as a split pusher because he kills towers SO fast (usually at level 16 I can kill an inhib tower in about 7-8 seconds), but he can team fight pretty well anyway. Taking teleport is a good idea if you aren't using ignite for kill pressure, because it allows you to do both really well. In a team fight, your job is to run at the other team headfirst soaking damage and clobbering their front line. You don't care about diving the backline, that's an assassin's job, what you care about is outlying the tankiest guy on the enemy team so you become nigh invincible and they become a wet paper towel. if your team can blow up the enemy tank quickly, you have a major advantage. That said, if the enemy tank isn't present or by some fluke you are already in their back line, go ahead and ult their carry since you should be able to kill them in only a couple seconds between your steroids, % HP damage, AA resets, and Trinity force procs. If an enemy is diving onto your carries, you can try to block them off with a well placed pillar so your allies can escape. You can also use your pillar offensively to separate the enemy team to allow you to slaughter their frontline while their backline is helpless to get to their aid. This strategy of dividing a fight is particularly good in the jungle because the corridors are so narrow and you can really throw a wrench in the enemy's positioning.
That's pretty much it for Trundle, just remember to use your AA reset correctly with Q and eventually titanic Hydra's active for maximized DPS, play aggressively when possible, and don't be afraid to take a seemingly bad fight if you have your ult since it can often turn things around really well.
Sorry for the long read, but I hope this helped!