Zed is a very mobile assassin who is more efficient than most of the others assassins/champions in the game.
The jukes will let you do some insane plays.

Zed is suitable to play many lanes : Mid, Top and Jungle.

Zed has a high damage output, as well as some great gap-closers with his W and R abilities.

Zed is a perfect champion for poke/harass/aggressive players.

Zed clear mobs very fast, is easy to lasthit with, intargetable during his shadow and ultimate-play, and simply very exciting to play.

Greater Quintessence of Attack Damage :
For Quintessences I take 3x Attack Damage for having that extra push early game, as well as easy last-hitting of minions and enjoyable harass-play.
Greater Seal of Armor :
For your early game/roaming you will eventually have to meet up with a AD-carry, AD-toplaner. Armor seals is the only option.
Greater Glyph of Cooldown-reduction :
While many prefer to take magic-resist glyphs for a safer teamfight/lanematch, I replace them with CD for that extra milliseconds of harassment early-game, and can easily compensate with your build later on.
Greater Mark of Armor Penetration :
Many regular AD champions/assassins will benefit more from pure AD stacking early game.
Zed with his already high Attack-damage output have no need for this and will benefit more from Armor Penetration runes.
Zed-math also indicates that this will produce a much more hard damage onto champions early game, as well as midgame-fights/lategame.

[+] 20 extra Attack Damage for your early-game.
[+] 4 Attack Speed
[+] 8% / 5 Armor Penetration
[+] 7% Increased damage
[+] 138 Health-Points
[+] 3.5 Armor and Magic Resist for easier match-ups.

The Bloodthirster :
- Sustain from lifesteal, as well as a quite high ammount of AD.

Blade of the Ruined King :
- Boost damage for your Ultimate,
more lifesteal to stack up with its 30 attackspeed boost.
It's active allows Zed to effectively chase important targets and deal a reasonable amount of damage.
(Stealing targets runaway-speed, dealing 15% of their maximum health,
as well as a instant heal equal to the 15% of the damage you are doing.

The Black Cleaver :
- This item gives you Attack-Damage, Health Points, Cooldown reduction, and Armor-Penetration.
This will help Zed with his survivability and his Tons of damage!
Armor-reduction and penetration-effects stack, allowing an attacking character to benefit from Black Cleaver's shred , penetration runes,
and other Penetration items.
Physical damage-over-time abilities will apply one stack on every tick.
The very first autoattack does not get the benefit of the armor reduction, which is no problem for Zed who will have alot of attackspeed as well as spamming combos and/or autoattacks.
The Percentage Armor reduction stacks multiplicatively with others champions Percentage Armor reduction abilities.

Last whisper :
- Armor penetration, against tanky AD champions, to melt through items like Randuin's Omen or supportive items like Aegis of the Legion.

This Item also gives Zed a decent amount of damage, but is sometimes a must-have caused by it's high armor-penetration.
Percentage Armor penetration stacks multiplicatively with others champions percentage armor penetration abilities.
Last Whisper becomes more effective at penetrating armor than :

- The Brutalizer when an opponent has more than 28.6 .
It becomes more effective than :
- Youmuu's Ghostblade at 57.1 armor.
It becomes more effective than 5 stacks of :
The Black Cleaver's debuff (+ flat pen) at 100 armor.

Warmog's armor :
- HP that prevents you from getting bursted down late game. This item is a item you also can get if early-game was rough.
You gain health regeneration equal to 1% of your maximum health, and +1000 Health points.

Frozen Mallett :
- This item will provide you with +700 health and +30 attack damage.
Zed's basic attacks slow your target's Movement Speed by 40% for 1.5 seconds.
(This will let you maintain your slowing effects from W,E ability-combo, when chasing a enemy.
Works well with your active from Blade of the Ruined king also.

GET THESE ITEMS IF :
- You are having a hard time with Crowd-control abilities/stuns:

Mercurys threads : cc counters most assassins

- Guardian angel : You are getting focused to hard and need the attention to switch to other targets (for you to safely cast your shadow out of there etc.)

- Randuin's Omen : Top/mid bruiser is feeded so hard and got a lot of AD/PEN going.
- YOU got feeded and want to have some funz :

Ravenous Hydra.

- Maw of Malmortius (Their mid/AP-Carry got fed hard) or you are getting countered by certain mages.
- In the front of your team :
Locket of the Iron Solari (Shielding yourself and your time for 5
seconds)

Passive :
Contempt for The Weak:
One of the most dangerous passives in the game.
Contempt for the weak gives your Auto-attacks a small burst damage after you drop the opponent below 50% health. (Often result in a duel-win/tie at least)
Also great for last-hitting minions.
Q :
Razor Shuriken :
Your main Poking and harassing spell. Try to hit your enemy without letting it pierce through any minions first. A lot of damage-potential, and a very nice ability to clear waves with.
(your shadow will shoot this ability with you) Always try to land these together (or hitting multiple targets at once).
Also smart to use from/towards/into brushes with your shadow.
W :
Gap closing and escapes. The jukes.
Makes waveclearing very easy, and works with your Q, E and plays between your R and W.
This is mainly what you will use as harassment and combo-play.
When to cast it and when you time to change places with your shadow is both crucial and hard to guess for your opponent.
If your team has lack of vision you will not want to cast this spell to early (ganked hard in the jungle).
This is also a fantastic spell for dodging abilities and faking what direction you actually will end up at.
E :
Shadow Slash:
an AoE slash with low cooldown. You will be able to cast this twice on your shadow if you cast instantly when the cooldown refreshes.
This combined with your shadow will slow your opponent and excels at clearing waves/jungle/buffs.
Useful at pressuring the lane, and since you got no mana you can poke with this w/ being afraid of missing. You will hit minions anyway. This counters a lot of mid-mages.
When your W is on cooldown, this ability will lower the cooldown : by 1 second for every enemy struck (HAVE THIS IN MIND IN CLUTCHING SITUATIONS).
Low cooldown, but it burns your energy-levels.
R :
Death Mark : (Indeed)
With the right combinations you will not know what just hit you, and how you just got cut from 100 to zero in few seonds.
This can also be used as a way to dodge ultimates (untargetable while you cast).
Works very well with ignite and actives such as Blade of the ruined king and the ghostblade.
The plays you can do with swapping places with your R and your W is EPIC.
This is like a Melee Leblanc with to much hp and razors attached to her fingers.

PROS :
Energy.
Gap/escape spells.
High damage output.
Poking/harassment.
Wave-clearer.
Last-hit friendly.
Intargetable with W and R.
THEM JUKES.

CONS :
Spells have high energy cost. (This you fix by grabbing the buffs in the jungle)
Melee.
Item dependant.

STRENGHTS > WEAKNESSES