If you already know how to play Zed but just want some more insight and a guideline for a build, this guide is just for you! This guide is nothing serious and it'll be very short and quick (I hope). I'm an amateur but I enjoy playing Zed and I've found this build work amazingly for me. I hope you have the same success with this build as I do!

Take 9 Greater Glyphs of Scaling Magirc Resist. This will help you withstand some of the heavier AP champs.
Take 9 Greater Marks of Attack Damage. These will help you haras your laner earlier, keep the pressure on them, and secure early kills because of the extra damage.
Take 9 Greater Seal of Armor. Extra Armor doesn't help especially if some sort of AD ganker comes in ;).
Take 3 Greater Quints of Attack Damage. Why? MORE DAMAGE!!!

21/0/9 is ideal on my Zed because you're an assassin, you gotta have that 21 in the Offense. These will maximize your burst damage and give you some CD reduction. In the utility tree it always help for me to have a bit of more movement speed for the roaming later on.

Boots 3 Health Potions are my standard especially to a squishy mid laner. If you feel very aggressive start with a Red Elixir but personally I don't like that start.
Now the items. Most Zed players I see build some whacky items and tbh it irritates me (this guide may also irritate you haha)
So rush a brutalizer always. It gives nice AD and armor pen. plus a bit of CD reduction. Not bad right? From here do NOT go straight into a Black Cleaver. Totally not worth it. You want more burst to kill dem squishys :)
Get a Bilgewater Cutlass, this will help with some poke because of the lifesteal and when you ult activate this on the ulted enemy, it should give you that extra burst from the Magic damage dealt plus a bit of slowing.
From here just finish the Bilgewater into a Blade of the Ruined King. This item is essential on Zed to maximize his burst damage. You steal movement speed making it easier to hit your E's and right when you ult when you activate this, when the death mark triggers the enemy ADC or APC will be instantly dead. Heck I've even tried this on an enemy assasin and killed him also!
From then on Upgrade your boots to Merc. Treads to help if you're stunned and to lower effects of slows.
Get a Bloodthirster for that extra AD plus lifesteal. This will tremendously help your burst and your AoE damage from your E and Q in teamfights.
Now you're thinking I'm pretty darn squihsy so now you get the Black Cleaver for some of that health plus extra damage, etc.
Get a Last Whisper to just completely ignore a lot of the enemies' armor. This item is amazing. Not only will it ensure the little armor an ADC or APC has be almost nothing but when you're one of the last ones standing you can go toe to toe with the tankiest enemies with your lifesteal and shred through the armor.
Now your last item is your preference I personally like GA over Warmogs only because if I screw up, right when i respawn i'll W to the closest ADC or APC switch positions ult blade of the ruined king and just do my full combo and hes completely gone.

Max E first
1. It's easiest to hit, does massive AoE damage and is on a low CD
Max W second
1. Many would disagree but the extra energy refund and lower CD really helps to poke down people.
Max Q Last
1. This move hurts but it's too much of skillshot reliant
Max Ult whenever
Duhhh

Flash helps you chase and escape
Ignite helps ensure kills

Honestly to lazy to do this part i basically summed it all up in the items. But let me rundown the combo for zed
Ult Blade of the RUined King the target, use E use Q, ignite
Don't keep chasing on thinking your Death Mark won't kill him/her but trust me it will or at least bring them so low they'll retreat.
Now from here the enemy might have collapsed on you unless you snuck around quickly kill their carry then snuck out. So to escape W away or flash or even use both if needed.
Now that you've escaped you can help your team finish the fight.

Just don't flame your team lol. And play as this guide has told you.

Pros
Deals massive damage
Great Assasin
Does heavy AoE damage
Really easy to last hit with
Is excellent in clearing minion waves

Cons
Kind of needs some early kills to really start snowballing
Early farming is important
Cleanse will remove death mark

The passive makes last hitting look effortless.

I HATE ZED JUNGLE!!!