Pros
Mobile
Very safe
Uses energy
Extremely high burst
Good for the entire game

Cons
High skill cap
Hard to come back if behind
Can easily be countered by escapes or items(QSS or zhonyas)

When you Q make sure you don't use it too early unless you know it will hit your target. When you go for the Death Mark, it is crucial that you hit your Q because if you don't, they will most likely survive. Use your W as a gap closer or and an escape. It can also be used in a fight to get more damage with a triple shuriken. Use E to slow to set something up. WEQ is a good way to harass because your E from the shadow will slow and that gives you an easy target to Q. Using your E in situation where it doesn't seem like you'll survive is very useful because for every champion you hit with it, your W cooldown is reduced by 2 seconds. Don't take this ability for granted. Your ult is what makes Zed very strong. You'll be able to safely 1v1 people because it provides an escape no matter how deep you go for 6 seconds. This let's you W aggressively and go for kills without having to die.

In team fights, it's your job to take out the enemy carry, or any vulnerable target. It's best to wait for all the major enemy CC to be used on the rest of your team. This lets you go in for an easy kill. Zed's cleanup on team fights is also very good so if you want to wait and chunk people down with your WEQ combo and go in when the enemy team is low, you can.
Zed is one of the best split pushers in the game because of his wave clear and 1v1 potential. You should be able to 1v1 anybody on the enemy by the time you are split pushing, so that forces them to send at least 2 people to stop you. This is when your team can take objectives.

Zed is very easy to farm with due to his passive. Unlike most champions who have to auto a caster minion once before they take a second turret shot, Zed doesn't need to. He can kill a caster minion after one turret shot with his auto. Don't be afraid to use your abilities to farm because they're on such short cooldowns.