RUNE BUILD

Grasp of the Undying is A MUST and the core of this entire build. If all that health is going to scale into damage, then Grasp is the way to go.
Obviously, Demolish scales with increased HP too and is the best option out of the three.
Conditioning is a free boost to resistances. You could potentially swap it for Second Wind against annoying harrassers, however, since conditioning also provides % increase for MR and ARMOR, that means it will be more useful even later on. My bias is towards conditioning, but second wind is quite a viable option too.
Overgrowth binds everything together by increasing you HP which will be converted into extra damage with grasp and titanic hydra.
When it comes to secondary runes there are many options. Their job is to complement main runes and the keystone. Precision and Domination runes are your best options to choose from, although Sorcery and Inspiration have their uses as well. In most cases your best bet is #1 Precision, #2 Domination with Sorcery/Inspiration sharing the #3 place.
As for minor runes, the ones listed can be considered the standard, but much like secondary runes they can be swapped as seen fit.

CORE ITEM SET EXPLAINED

Hullbreaker is a massive boost for any AD top laner. Its most well known and bought for its unique passive effect to increase sieging potential and add resistances. However, it also provides great stat boost to AD, HP and HP regen. All this makes it a fantastic all around item. Acquiring it should be prioritized ASAP.
Titanic Hydra converts every health point into damage (much like keystone Grasp of the Undying, this item is crucial in gaining damage while still getting tankier) and provides cleave for farming efficiency.
As far as Boots choices goes, these two are straightforward defensive boot choices. Buy whichever is more suitable against the enemy team.
Kraken Slayer is the Mythic item of choice. Its Stats, Mythic bonus and True Damage effect are all great additions to the arsenal. Since its True Damage effect scales of AD and AD will scale additionally from TH's passive effect (HP to AD conversion), that means there is a sort of "two for one" scaling - more HP and/or more AD results in more True damage from Kraken Slayer.
When it comes to item order, I'd go for #1 Hullbreaker, #2 Titanic Hydra, #3 Kraken Slayer. Kraken Slayer won't provide as much of a power spike as Hullbreaker + Titanic Hydra combo, beacause of Grasp keystone and TH converting effect and an obvious massive HP boost for survivability in fights. Thus, Kraken Slayer goes after those two. As far as boots goes, fit them in early on, even before Hullbreaker and even if you have the advantage (you can always make the power gap wider).

HULLBREAKER: SWAP OR NOT?

Hullbreaker is the sweetheart of many top laners. Unfortunately, this sweetheart doesn't share, nor tolerates ally intruders while providing these benefits. Fortunately, this Tryndamere invests heavily into brusier items and doesn't need his allies assistance (or not as much in the very least). So, there are benefits, but there is also a catch: Hullbreakers increase to AD, HP and HP regen will remain if allies are nearby, but the seige damage bonus, canon minion buff and resistances buff will be lost, and, thus, as Shakespear would put it: To swap, or not to be swapped, that is the queston. This is, of course, reference to his play Hamlet, where Prince Hamlet contemplates suicide, while weighing his life against death. Same goes for Hullbreaker (albeit far less dramatic).
Now lets talk some options.
KEEPING THE ITEM: Its unique effect will be lost in teamfights, but its stats will remain and they are worth keeping. Obviously, you can solo enemies, split push and achive its full effect that way. Hullbreaker isn't a really expensive item, so obtaining it isn't that hard and selling it won't make you rich, but it could provide most of the item components for other legenderies. From the "economic" perspective it is worth more kept than sold. It is certanly more economic and beneficial to keep it until the full build is completed.
SELLING THE ITEM FOR ANOTHER: In case you decide to be more teamfight present, you could do much better than to keep Hullbreaker. For example Sterak's Gage grants more AD, same HP but also a shield. Tryndamere likes his critical strikes, so an Infinity Edge is a massive damage boost. If your damage is solid, but you desire more health and regen, then go for Warmog's Armor. Grab Maw of Malmortius against AP bursters. Maybe you want to prepare for every teamfight and have Undying Rage ready - take Axiom Arc. To put it in a nutshell: take what you need depending on how well you and your team are doing.

SUMMONER SPELL COMBOS

IGNITE ROUTE
Ignite's DoT and anti-healing effect can turn the tide of battle against harden champions, or help in securing a takedown. Consider this if you plan to farm enemy champions like minions (yes, you do!). Flash and Ignite can be considered a standard and provide the greatest benefit in most scenarios against most enemy top laners.
TELEPORT ROUTE
Teleport provides greater opportunities to set ganks and farm lanes which enables you to reach the Core Build faster. Consider this if you plan to focus on pushing hard and attending teamfights last-minute. In late game a well used Teleport can potentially end the game. Early on, its really only useful to get back to your lane faster, but that can give you an advantage against your opposing top laner.
EXHAUST ROUTE
This a duelist and escapist combo. Exhaust can single handedly ruin enemy team junglers gank or secure a takedown with an ally jungler. It can also turn the tide of battle in 1v1 against enemy top. Consider this in same scenarios as Ignite. However, think of it more as a defensive option, although it can certanly be used to run down your enemies and for ganking. There is no doubt that running Exhaust will make you much harder to kill.

EARLY LANING AND STARTING ITEMS

SHIELD, BLADE OR CULL START

If you've been reading the notes and you possess some common sense, then you've probably figured out which starting items to take based on your match up. Nevertheless, here we will dive in a little more detail regarding these item choices and how to set a strong tone while laning early on.
As mentioned, Shield is your best friend and safest route to take. It levels the playfield against those who harrass and also bought a Shield of their own. Maintaining a strong lane pressence is important in order to gain an advantage. Take sort of a 'slow and steady' approach when laning with Doran's Shield. You can afford to trade more and harass your opponent.
If you are having a really easy time laning, consider going for Cull. You can grab Future's Market as well and build a gold empire right from the start. Farming is the name of the game with Cull. This is the riskiest item route to take and it is heavily influenced by the enemy team composition. Avoid it if you won't be able to farm minions quickly.
For every other Tryndamere a Doran's Blade would be a route of choice. The Blade is less defensive than Shield, but safer than Cull. Overall, if want a more reliable item and to be more aggressive, then take Blade instead of Shield or Cull. Play in a similar fashion like you would with a Shield, but since it provides omnivamp, a defense is an offense.

EARLY LANING

Now that we settled the items, it is time to put them into action. I'd like to define what 'early laning' means. I believe most people define this stage of the game based on a game timer which is in tight correlation with game events. Examples include turret plating period or dragon , rift herald and baron spawn. I like to define game stages based on ITEMS OBTAINED and LEVELS REACHED. Combined, they form a POWER SPIKE. This applies to you, ally team and enemy team. Also there is a certain 'feeling' during early laning stage: a sort of a Parrrley period where both top laners focus on minion clears, wave menagment and getting a plate here and there with some poking/trading. At some point all this becomes secondary and every time you meet your enemy top laner you primarly engage in combat with an intent of scoring a takedown. This happens once a power spike is reached for either or both champions. That 'cozy' feeling is gone and so is the early stage. Keep it safe, but focus on shoving waves. That will allow you to get more gold from turret plates and deny some minions for your enemy under their turret. This playstyle will draw attention onto you and the enemy jungler will respond to it. This is where the safe part comes in - ward proparly. Placing a stealth ward near heralds/barons pit or at the blue buffs jungle entrance instead of the river brush will reduce the chance of enemy top dewarding it. Also, invest in a few pink wards. You can grab one as early as your first back.

GRASP TRYNDAMERE'S POWER SPIKE

When it comes to levels, a power spike is reached at level 6 with Undying Rage. Quite similar to other Tryndamere builds. If you selected Last Stand for one of your runes, your ultimate will make its use more reliable. This ability requires perfect timing and it can make or brake a fight.
When it comes to items, there are some deviations based on match ups. If you are having a really easy match up, then Upgraded Boots and Hullbreaker will be sufficient for a power spike. In most cases, I'd say a Hullbreaker with Upgraded Boots and Titanic Hydra will provide the desired power spike. In severe cases, you will need an entire CORE BUILD to reach a power spike. So you either reach the power spike AT/OR PRIOR TO OBTAINING THE CORE BUILD. If you reach it prior to your Core build, then procede to use the advantage to reach the Core set faster.

THE CORE ITEM SET AND MID GAME

This will mark the period of 'mid game' for YOU. Playstyle still remains pushing/shoving oriented but more opportunistic and team focused. If your team seems to be falling behind, then be more team present. If they are doing fine without you, focus more on solo play - shoving waves and applying lane pressure (check the Hullbreaker section). Clear enemy jungle camps if/when you can. This puts pressure on the enemy jungler (duh!). Finding the right balance between 'solo' and 'team' play is crucial. As you work towrads the final two item slots, along side other map objectives, you will reach the late game.

LATE GAME AND THE FINAL STAND

This period is marked by having a full build (check for some of the examples above) and teamfight clashing. Combination of mentioned rune and item choices transform this Tryndamere into a powerful bruiser or even a semi-tank (THE BEHEMOTH build for example). As such, your job is to get hit in a face a bit while dealing damage. Since Tryndamere lacks real defensive options regarding his abilities (and has offensive + utility ones instead), your job is to BOB AND WEAVE in fights while trying to take down key targets in the enemy team (such is their Mage or ADC). Tryndamere's ultimate can't make up for poor positioning and target focus. Once again, use it wisely. In general you will have more survivability than your average Tryndamere, but will also lack some burst damage potential. Thus, it is important to be able to deal consistant damage. Increased survivability allows for another option (although, sometimes a desperate one) at this stage and that's a FINAL STAND - basicly being outmanned and outgunned while trying to take a key objective/target against the odds. Note that this shouldn't become a suicide that will leave your team with one champion short (and even cost you the game in the end), but rather a precise move to gain tactical advantage., such as taking/stealing a (eldar)dragon, baron or destroying turrets and inhibitors as a one man army.