Hello and welcome to my Solo Top Tryndamere guide! First off, I want to tell you that Tryndamere is a very situational champion, and should only be picked when you know that these two things are 100% true:
1. They have a jungler, and top will be a 1v1 lane
2. Their top is not malphite, nunu, or nasus (If it is one of these, take cleanse + ghost).

I know that these masteries are a bit weird, but Tryndamere has three very awesome qualities that allow him to take 25 points in the Offense Tree:
1. He has Magic Resist gain per level, which is very rare for a melee carry.
2. Tryndamere at level 18 has the third highest base health in the entire game (after Nunu and Sion).
3. Tryndamere snowballs hardcore with any type of damage.

The runes are pretty straightforward:
Marks: armor pen is great because if Tryndamere builds any type of armor pen items (ex. Last Whisper, or Youmuu's), Tryndamere loses out on a lot of damage.
Seals: In top lane, bruisers like Riven are very common, so any armor Tryn can get is very useful, and critical chance / attack speed seals arent worth the loss of the armor.
Glyphs: Two types of glyphs can be useful here: Magic Resist per level and Cool-down Reduction per level. I take Magic Resist per level because it stacks well with Tryndamere's passive Magic Resist per level.
Quints: three types of Quints are acceptable here: Armor Pen, Attack Speed, and Movement Speed. I take Armor Pen because, again, Tryndamere needs the armor pen to deal with Thornmails, but cant afford to lose too much damage by building armor pen items, so runes and masteries are a good resource to get armor pen from.

Now, as I said in the Introduction, Tryndamere is a very situational character. This means that almost any item will do for starting out with. My recommended starting items are:

Boots + 3 Health Pots (Against a Karthus or a Nidalee)
Armor + 5 Pots (Against an ad bruiser or Garen)
Doran's Shield (Can be bought in place of cloth armor, but sometimes not the smartest choice).

Other starting items like Doran's Blade I don't recommend because of the lack of sustain. Vampiric Scepter can be good, but it can also fail hardcore against someone like Shen or Teemo that can deny you the melee hits you need to sustain yourself.

The skills on Tryn are very simple:
1. Spinning Slash is for damage at level 1 or for escapes, but does not need other levels until there is nothing else to get points in.
2. Bloodlust is your major source of damage and healing, so it is very important to max it first. Bloodlust also works very well with Tryn's ult.
3. Mocking shout is a hard counter to AD carries, as it lowers AD, and is more important to max than Spinning Slash after Bloodlust.
4. Some Tryn players argue that only one ult point is needed, but if you max Bloodlust, the extra fury is amazing right when you activate it (especially for crit chance).

Now, I take exhaust because of two reasons:
1. It is an amazing spell for shutting down carries like Ashe and Vayne that can burst your teammates late game.
2. Even though Tryndamere already has a slow, if the opponent wants to right you, they will not turn around and therefore, will not be slowed.
Flash is awesome for two reasons also:
1. You can troll people with a double flash (Spinning Slash+Flash) to chase them or to get away.
2. It is a good spell to have in case you have to initiate with Spinning Slash.

If played correctly, and in the right circumstances, Tryndamere will snowball hardcore and will dominate top to the point of their team surrendering.