Pros:
Good at bursting down squishies
Innate escape built into his all-in combo
Lane bully
Hard to gank
Energy instead of mana
Low CDs (Especially late game)
Can get kills in lane and make the game impossible to lose early

Cons:
Difficult to learn
Especially reliant on using combos right
No CC
Experienced players can predict Zed
Ultimate reliant (To some extent)
Hard to use if behind

Early Game lasts from the moment the game begins until the first towers fall and people begin to swap lanes. This is the part that will determine whether or not you will be able to knock your enemy laner out of the game.

LVL 1: Farm and poke a little.

LVL 2: I usually add a point in W for extra safety/damage. Use your W to farm if the enemy is bullying you or for poke if they aren't.

LVL 3: Put a point in E,or W if you haven't already. Use your W-E-Q combo to harass the enemy laner every time they try to farm. If they get low enough swap places with your shadow after your combo lands to try to finish them off with your passive and ignite.

LVL 6: This is where you become a real threat. By now you should at least have a Serrated Dirk, this is extremely important, the extra lethality will ensure you get kills. If the enemy midlaner hasn't hit level 6 consider attacking them. You usually should. From this point onward you want to use your basic trading combo to kill your laner a few times, then look for a roam.

Roaming takes practice. If you've played jungle a lot you'll know when a lane is good for a roam. However, you want to push your lane as far up as you can before you leave lane. This will reduce the amount of CS lost while you're gone. Then you want a target. Usually this will be your bot lane, since top laners are typically too tanky, but there are some exceptions. Basically you want to avoid any wards either by walking around likely spots or with your Duskblade, then ult on the ADC and kill them. Their support will usually run for their tower if you succeed. If you can't reach the ADC, killing a squishy support can help your bot lane too. Assuming you succeed, you can then help them push to the tower or return to your own lane, potentially getting another kill if your laner is overextended. Remember that your jungler can help in this too! Few bot lanes can survive being ganked by two champions, and an overextended midlaner is just as likely to die.

Mid Game begins when the first towers fall and laners begin to swap lanes. This is when Zed begins to shine. You want to punish every isolated squishy. See a Jhin all on his own down in the bot lane? Kill him. No ADC should be able to win unless you make a huge mistake. However, you don't just want to watch the squishies. It's just as important, if not more to track the rest of the enemy team. Judge how likely an enemy jungler is to intervene if you attack one of their carries. Also keep in mind what they have to use against you if they do appear. A Riven will be able to change the situation very quickly, but a Soraka will only be able to watch as you kill their ADC.