What this build should do. early game farm and poke enemies to keep em off you. the boots and health pots should keep laning. for a while enough to get up in level. Once you have enough for mercs treds finish off the minion wave and buy em. next you need to bet enough to buy brutalizer. if you have extra when you went to get your mercs treds and can get a long sword do it. if not wait till you have enough. after getting the brutalizer then killing should be much easier the cooldowns will help with your combos the armor pen is just nice to have and the dmg is good for an early item. next go into sheen. seeing as how zed is a massive ability user sheen sheen should help destroy enemies when bursting. next go finish tri force in any order you see fit. i personally recommend phage fir the health and slow buts its what you need at the time. having a tri force will make you a force to be reckoned with... this doesnt show in the build but if your having more issues with health rather than dmg go for the blood thirster first but make sure you get the "Best Friend" sword first. then you go from there what you need. once you have both the BT and IE done get a hexdrinker. if your having much issues with mages then get the hexdrinker after your first power item (BT or IE) its now up to weather a ghost blade is more useful or a maw is. go from there at the end you should be 18 before most people and you dmg should be around 500. now what? now go be a flippin Ninja and murder everyone.

Side Note he can back door really well.

Early game
While in mid farm as much as you can. Use your Q to back enemies off you while you farm. Remember that Zed has no mana and use his abilities as mush as he wants. use living shadow at the other end of a minion wave use your E then Q between them dealing max damage and finish with E again. this should wipe out the minions with ease. Zed shouldn't try to kill any champs until your at Lv3. While in mid occasionally take time to hit near by jungles to get an extra boost. this should help with gold and level. any enemy encounters should be short and result in their death or their retreat. Use living shadow behind then then your slash to weaken and damage them. Q then E again and if they arent dead they'll be running. also keep in mind that as a fighter zed has great range so if your low on health stick it through and have your shadow farm.

FARM FARM FARM

Mid Game
By this point you should be high in level and well on your way for your build. you should have a turret or 2 in your lane gone by now. so jungle here and there keep farming and any enemy alone in your sights should be dead with a burst. your ad and armor pen should give you a slight edge, not that you chew through casters like no tomorrow. Be wary of bruisers if you dont kill them in 2-3 busts you will most likely die. the draw back to Zed is his health as a fighter. He's an in then out champ.

Late game
Your build by now should be done. still be best to have caution around tankier champs that do damage or any champ that can break your combos. your main job is to run around and assassinate anyone alone or weak.

Gauging how to kill enemies with your passive
Aside from getting this build down. Remember Zed's passive lets you destroy enemies below 50 percent health. after getting a feel for zed. you should be able to gauge enemies weather or not you can kill them. even if their health isnt at 50% consider how much damage you do and how low you can get them. the point is to lower their health drastically then with combos and melee to murder them. this is a great skill. you can look at an enemies health and immediatly know if you can kill them on the spot.