Notes

Here's a read:
Armor pen on your runes, flat AD on your items.
You want your first back to be Tiamat if you started with longsword, or Boots+Pickaxe if you started with Crystal Flask.
Abuse his low E cooldown. Blinks as long range as that don't typically have <20 second cooldown and it catches many players off guard. Enemies also sometimes have a hard time learning its distance. If you alternate between holding onto it and spamming it, you can really throw someone off.
When you level up to 6, basically just use your ult within 2 seconds if you have above half your mana. You want to just throw down your full combo on them without commiting for the kill. Blow their summoners but not yours. Then in ~15 seconds when they think they're safe because you don't have ult, go in with the standard combo and all your sums for the kill. This works best versus immobile mages, or targets that think the're safe because they have cc, but you can blink over the skillshot (Think Xerath E, Lux Q, or Morg Q).
You want your early items to be Tiamat, Yomuu's, and Mobi Boots, in that order of priority. With this setup you have really good flat armor pen to counter any early armor (Supports with full armor runes or junglers getting their cinder+warden's mail) and you have everything you need to go for any type of kill as Talon.
Basically the different kinds of kills are...
1.) The Perfect Combo: Yomuu's, E, AA, R, Q, Tiamat, W, AA, Ignite. This does the most damage possible in the shortest possible amount of time. If you have <50ms ping and good timing, you can complete this whole combo in about 1 second and it can do upwards of 4000 damage vs 120 armor targets in the lategame if you get crits. This is what you do to win your team the teamfight, and then die. You essentially instagib 1 person, do decent damage to another 2 or 3 targets, then you die. Can't really help it unless you buy GA or Mercurial Scimitar. No shame in that though. It wins fights, but always make sure your team is behind you.
2.) The Splinter Cell: Yomuu's, E, AA, Q, W, R, Run away, R. This combo does okay damage and gets you out of there alive. If you do it correctly then the yomuu's speed boost should stay up long enough to stack with the R speed boost, meaning you are GONE. If you can dodge their skillshots and avoid AoE, then you will also have Mobi passive kick in right after coming out of stealth. You wanna use this when you're pretty fed vs a team with a squishy target as well as point and click CC. You can just get in there, kill them, and get out. Never use this if they have Pink Wards or Lee Sin or whatever unless you are VERY confident.
3.) The Assassin's Creed: Yomuu's, R, E, AA, Q, W, Tiamat, AA, AA, AA, AA, AA... Basically you go in as stealthy as possible, but once you're there you just try your best to kill this one guy and if you succeed then you're good and getting out doesn't really matter as much. You might as well sit around and try to swing your sword at things until you aren't in risk of dying any more. You do this versus immobile hypercarries that need to get out their DPS over time, but have like zero burst. Think Ashe or Cassio, except when their ults are down.
4.) The Ninja Gaiden: Walk up to someone (or wait in a bush for them to get close), AA, Q, Yomuu's, AA, W, Tiamat, R (You use this R to dodge damage and skillshots), AA, Run around, E, AA, Q. This is for killing people that you have no right to be killing, like Vayne or Tryndamere. It's really risky and stuff, but it lets you compete with AA DPS Crit machines that you can't one-shot. It's also good for more extended fights or if you're a bit behind and you need to do as much damage as possible. High risk high reward.
And just the complete Item guide in case that's not obvious...
Starting: Crystal Flask+Pots vs waveclear or shit matchups, Longsword+Pots vs easy matchups, and Boots+Pots vs skillshot whores.
First back: Tiamat, Pickaxe, or 3 Longswords in that order of preference. Only get boots after getting at least one of those.
Core items: Tiamat, Yomuu's, and Mobi boots. Never upgrade Tiamat until lategame.
Mid-Game: LAST. WHISPER. After that you can get a Hexdrinker OR Phage, which you will want to upgrade into Maw/Cleaver as you get into...
Late Game: Finish your Maw/Cleaver, then get the other one and upgrade your Tiamat if you're snowballing. If you aren't strong, consider grabbing GA if you're getting bursted, Randuins+Cleaver if you're having to stick around long teamfights, or Mercurial Scepter if you're doing really well but you can't fucking do shit because they have a late-game Malz/Morg/Ashe/whatever.

Your Masteries are 21/9/0. Spellweaving/Bladeweaving is overrated. Basically get all of the second row of offense tree plus double-edged sword and Deadly Game. Get the 5% CDR and 5% from runes. I think you also need 2 points into either the attack speed (helps csing) or the feast thing (helps survive hard lanes if you're good at csing). It's preference.

You need 3 rune pages. Both will have AD Quints and Armor Pen Reds. I've seen some people run 2 AD Quints and 1 Armor Pen Qunt on top of the Armor Pen Marks and that seems okay as well, though Csing is harder.
As for the other parts of the 3 pages...
One has Armor Seals, 6 CDR Glyphs, and 3 MR/lvl Glyphs.
One will have Health Seals, 6 CDR Glyphs, and 3 Flat MR Glyphs.
The last one will have Health Seals and Flat MR Glyphs.
The first one is for fighting AD midlaners, the second is for fighting standard AP carries, the last one is for holy shit fuck me they picked Swain/Vlad/Fizz/Heimer/Leblanc/Mordekaiser. Typically if you run that last rune page, you also start flask, rush hexdrinker+tiamat before getting yomuu's, and buy a GA right after Last Whisper.
Everything else you need to learn Talon comes from experience and learning your limits with the champion and what you can and can't get away with. Also roam as soon as you get mobi boots+tiamat. Earlier if you're not in a good lane.