Hello, name's CCyde and this build is not aimed to new players.
I've been playing League for long now, and one of the first champions I got (if not the first, I hardly remember)was Tryndamere. It was my main for a long time. I got really good with him that I always tried to pick other champions when playing with friends to not get bored for the easy game (not kidding).
So, I'll write this guide supposing you know the basics to play Tryndamere.
I'm skipping basic introduction to the champion, and I'm going direct to the topics here: How to enhance your gameplay in this new season. Along with the new Runes Reforged and some personal tips I hope can help you.

I mostly play tryndamere in top line. I'm focusing on this position this time. And will add a "jungle" section later on.

If you've been playing Tryndamere you know that early game you are way stronger (and dangerous) than most your opponents at top line, even tanks can't withstand a couple of crit-hits induced by your passive when you are at full Fury (red bar).
And note that most times you get to take your hands on an opponent with your full Fury they just get away and escape spending Flash or with help of their jungle pressing on your back.
That's when you realise you lack a mspeed boost on early game.
I used to take the "Ghost" Summoner Spell instead of Teleport almost without exception. Ghost is a really good but understimated summoner spell. With Tryndamere it went perfect because of the 10 seconds movement enhance. That's plenty a lot of time you can use to chase your opponents or/and get away to safety.
Ghost always assured me the first kill. Playing your fury, E and flash smartly could even get you a second and third kill just with your starting items.
Sometimes you will end up chasing enemies to their tower and there's the perfect time to use your mspeed boost and then (E) to go through the tower if they try to be slippery. If you play those cards well you'll kill them and then withdraw successfully using (Q). (Use Undying Rage(R) if necessary at emergencies)
Now, about returning to your line when in a hurry, again, Ghost has just 180CD and you have your Spinning Slash that takes you through walls too and costs you nothing.

As well, you could use your Mocking Shout(W) before to delay and chase your enemies after they flash to escape but it was never enough and to make it efficient you had to sacrifice your Spinning Slash(E) upgrades. Or wait till you get that Blade of the Ruined King to help you there.

But the future is now and Runes Reforged has bringed new ways to everything.

To begin with, Now you could use Teleport Summoner Spell instead of Ghost. Ghost is still pretty good but is more situational now.

To compensate our mobility, we are are choosing "Inspiration" as our Primary Path and taking "Glacial Augment" as our Key Rune, this rune is great and will help us when Mocking Shout is not enough.
Then there's Magical Footwear and Approach Velocity will give us the other mspeed boost we need to move freely whether to chase or keep us alive and ready.

You'll want to take Future's market to get our items way faster early game.

Taking "Precision" as our second path will give us passively +20%Attspeed.
You can boost that taking "Legend: Alacrity" or "Legend: Bloodline" instead if you want more sustaining.
Finally we are taking "Last Stand" because of course! just read the rune is obvious we are taking it!