I used to play Tryndamere in S4, it's how I got from Silver to Gold. And i'm recently starting to play again because people I feel have forgotten about his insane dueling potential even without kills(being 0/7/0) for example and 2v1'ing the jungler and top laner. (Careful now tho with the new Juggernauts, Darius will wreck you, and Garen will be a bit stronger against you aswell) I've learned that trying to fight lvl 1 to assert lane dominance is a good stradegy as long as they are a champion that doesn't have a good lvl 1 or health rgen. I try to do on blue side mostly. since the tri bush in top lane is "theirs" I rush to that bush. and I wait to see if the enemy top laner will run through there, if they do I start e and I auto them and when they get out of range a bit I e to get some more dmg off. When doing this wait for them to get right infront of you at the bush. don't come out to them. because then you lose out on the surprise and free auto for being in bush and unseen. If they don't run through the bush i usually start q in that case. so I can cs and heal up. Yes using your q isn't the best because you lose rage. but the heal is nice to have, and should be abused more to keep yourself healthy.
Also, take tp. no matter what take tp. if you want ignite, get rid of flash. because tp is the most important thing on tryndamere. Being able to back and tp back into lane (even if it isn't the smartest because you lose dragon control.) is so helpful to surviving lane phase with tryndamere. and as you should know. having tp opens up the split push with Tryndamere late game, and carrying the game by yourself.
But in lane phase against ranged champions like ryze, gnar, kayle, teemo, basically you just play at max xp range. and get what you can with the least amount of harras. and wait for jungler to come help. Gnar though you will learn you can actually abuse lvl 1 if he takes q first and you take e. since he won't have a jump. or the auto attk bonus from third auto. all you have to do is dodge the q and and e onto him when he flashed or is to far away. this can get you lane dominance so easily, and honestly works with all of the ranged champs accepty teemo. becuase if teemo starts blind, then you're kinda useless and its just annoying. and if he starts e he will just auto you to death, and win the trade because poison dmg. teemo is just a bitch lane for you and you wait til lvl 6 to try and do anything and even then. you have to be careful cause he can kite you so easily.
For melee champions that "counter" him like Darius(another bitch lane for you because new rework and Darius is just a monster), Riven(Just have to outplay her and fight when she is on cooldowns.), Jax (yeah his e is a bitch). Laning against the hard melee champions. its okay to stand up and farm, but if they look to fight. unless you are stronger and know it, just e away if you have to, because they will win a fight 75% of the time. Like I said with Darius, You just play passive, his Q harass is insane, and if he does that consistently and then pulls you in, ur gauranteed dead of using flash, wait for jungler, or just wait for him to kill your tower and roam, because lets be honest, he isn't your problem if you don't feed him. if he gets fed becuase your team is fighing 4v5 thats there own dumb fault for not waiting for you to get a good splitpush going. Yes, the mentality of that sounds bronze, but Tryndamere is just that champion. you have to just split push and do small skirmishes, because teamfighting with tryndamere just isn't a thing unless you're fed to all hell and can 1v5 them. You have to just split push and wait for enemy to send someone and kill that person, or they send 2 and then your team is able to fight 4v3. (this is something people don't know though, and so if you are just even with the enemy top laner, prepare to be flamed, even if you win the game through split pushing. people just don't understand split pushing, and they think it is a troll stradegy becaue you "aren't" helping the team. even though you make it a 4v3 for them and then you are getting map pressure and global gold because you are getting towers. and you get dragon control since they have to send 2 or 3 people up to you to stop you, becaue one person, unless they are fed can't stop you. Once you get Shiv, Bork, and Ghostblade or IE, you are basically the strongest in the game and can 1v1 anyone equal or slighty ahead of you.
Sorry I ramble a lot haha!!! But Tryndamere is just learning matchups learning how to play the matchups and gettting the most out of the worst. as dumb as it sounds You just gotta play him and play him against as many champions as you can so you can learn wht happens and learn what to do instead. Learn how to play passive, learn how to fight lvl 1 to assert lane dominance but without losing it yourself, and then try to explain to your team that tryndamere can't team fight well and then they need to create options for you to split push to draw 2 of the enemies to you so its a 4v3 for your team. or just get map control, yes you will get flamed a lot! but lets be honest, people will flame anyone who does feeds and still carries, just because they fed. no one will acknowledge that you are why you won, except for the enemy team. because they lost to you. even if you go 0/10/0 but you got 5 towers 2 inhibs. by yourself and your team got the teamfights they needed because it was 4v3. you did your job. who cares if they are mad, you are allowing them to win the teamfights. and the just win the game. All in all, learn the matchups, assert lane dominance when available, don't fuel your teammates rage against you by raging back, just simply explain how tryndamere works, and learn to play passive in lane phase A LOT!
Hopefully this helps, Sorry its long haha! Like I said I ramble, but I tried to make it to where everything I said you had something to learn if you didn't know it! Good Luck!
Believe me. Good Luck Have Fun.