Uncancellable, becomes untargetable when he already has crazy mobility, and nukes about a third of my health at like, level 8. Without me having already fed him and with him having died twice. Like???? All he has to do is appear out of nowhere and press R
EDIT: zed mains can relax, i'm not hating on your champion. i'm asking for advice. log off and go outside please
If you're going against Zed, bring Exhaust. Just do it. Don't bring Ignite, don't bring Barrier, take Exhaust.
When he uses his R, smack him with Exhaust as soon as you see his ugly mug reappear, and run away. It reduces the damage he does to you and slows him, so when his R mark pops, that damage is double-reduced.
If you've got a skillshot, aim it behind you right as Zed is going to reappear. He always reappears behind you, like the stupid weeb he is, so using his R opens him up for whatever stun or combo you can throw at him.
If you're a mage, rush Seeker's Armguard before your main item. Build it as fast as you can. The stacking armor from it negates the lethality from two (2) of Zed's fully-built items, just by itself. Turn it into Zhonya's after you finish Luden's or whatever, and you'll have another button you can press to save you from his R.
put a range limit on his R blink back
Ever since they removed that bullshit extra passive, which was that Zed inherits part of the victim's AD if he kills him/her with the ult, his ult isn't that bad.
I dont play Zed, but when I do I press R and roll my face on the keyboard and get a kill and am back safe under my turret.
honestly just kill him harder.
Zed is not a good champion design. He can make countless mistakes without being able to punish him, but if you make 1 mistake your lane is over.
It should be a skillshot.
Or does the ''should be an skillshot!!'' bandwagon ends when it comes to assassins?
Depending on who you're playing, you can deal with Zed's R fairly well (champions that can punish him for getting close, shield themselves, leap away from him to cause him to miss things, etc). Otherwise, you're purely working with outsmarting and proper itemization.
First, look at his ult--> He presses R, and it takes 0.6 seconds of untargetablity for himself to show up behind you (following you during that time). He always shows up behind you (e.g. YOU will be between him and his shadow from where he ulted from). It gives him an extra shadow, which allows him Q's, a slow from his E, and a blink with his R again 0.5seconds after he lands. Damage he does to you is reapplied at a reduced value after 3.0 seconds.
Knowing this information is really important in order for you to know what your options are, how to dodge damage as best as you can, and how to punish him as well.
1a) He is now in melee range and his R is locked for half a second before casting it again, opening him up for a melee attack or short ranged spell) 1b) He will land in a known location, setting him up for a skill shot.
2) He is more than likely going to try and make use of his ult to damage you, so you can be sorta confident that damage will be coming (Not always the case. Good Zeds use their ult as a way to dodge things or kill very low target they are chasing when they don't have other options, leaving their basic skills to kill targets, typically). So either he's going to hit you a lot, or he just wasted his ult to be cool and trick you. **2b) **Zeds love being able to go in, kill you, and get out ASAP, to reduce the chances of him taking too much damage or being CC'd or caught out. Armor + health is great because it means he needs to get out more damage to you, which may mean more AAs which means more time next to you before he R's away. During this time, he allows himself to take more damage by being in your range, making him more vulnerable, OR, he just gets out and you survive.
3) You know where his shadow is (from where he luted from), so leaping/flashing away as from that original location reduces his potential damage. Time the leap/flash properly to get away from his first shadow and from where he lands. Do so too early and he follows with you.
**4) **Since a % of his damage comes from having a delayed burst after 3.0 seconds means you can predict a burst of damage. Items that provide shielding or invulnerability counter him. 
As previously mentioned, armor is never a poor choice if you can afford it.
These are some things to keep in mind!
Assassins hard counter ranged casters so hard most are stuck in support roles (Zyra, Brand, Xereth, Vel Koz, Swain, etc.) and if you build something like Arm Guard your losing out on sustain and clear you need for laning.
--> there you go the champion can't touch you anymore.
Uncancellable, becomes untargetable when he already has crazy mobility, and nukes about a third of my health at like, level 8. Without me having already fed him and with him having died twice. Like???? All he has to do is appear out of nowhere and press R
Technically, Zed R is cancellable. First of all, Zed R has an auto-cancel inside itself: "If the target dies or is 1950 units away before the dash begins, Death Mark is canceled, goes on a 5 second Cooldown, and Zed reappears at the cast location." (source: LoLwiki). Every Zed main knows this. Moreover, there are some abilities (e.g., Fizz E) that, when properly timed, can actually cancel Zed R, as shown in this video: Link.
Since other people already answered several ways to counter Zed, I am just going to post some champions which have kits who counter him really well: 
, 
. If played in a proper way, 
and 
cannot lose lane vs Zed. Other than that, one of the "tricks" Zed can do is Zed's all-in at level 3, with full-combo and 
. Some players cannot anticipate this burst and get a "surprise!" effect when they die. If you are at about 65% or below at level 3, know this can happen. The second "trick" Zed can do is to be really careful about EXP, anticipate level 6, take R and use R instantly (when enemy is still level 5, just barely away from level 6). This is an old trick and relies again on the "surprise!" psychological effect. Good players know this can happen and so are more careful.
Most tanks can also handle Zed and ignore most of the things he can do (despite what someone said regarding Zed doing a 100-0 to Poppy, that can happen only if Poppy's player is bad or Zed is really ahead, and it's not going to happen when both are full build).
Talking about Zed as a champion, I think he is (right now) slightly on the weak side of the power spectrum. There are assassins which do what Zed can do, but just better, faster and even more reliably. Pre-nerfs Akali was just Zed 2.0 (or even 3.0 if we go back to when Akali had "true invisibility", one of the most broken mechanics in the whole game, which was in fact removed).
Back in the day, I played Zed for many many games and I did not agree with the removal of QSS as a counter to Zed R, I think it was a really bad decision, especially for ADC mains in low elos (where you can't rely on your team) and stopwatch didn't still exist. I also did not agree with the "delay" in Zed R swap-back, it was (and still is) just nonsense and killed some combos which required skill and quick timings.
Zed late game isn't bad, but it isn't stellar either.
IMHO, Zed should receive a small QoL buff. Zed W has this (source: lolwiki): "Zed restores Energy whenever a Zed's Shadow lands a mimicked ability on the same target he does. This may only happen once per cast ability." The sentence "This may only happen once per cast ability" should be removed: in late-game, sufficiently short CD may occasionally allow to proc E (or Q) two times on the same target. It is neither a common occurrence neither guaranteed. Refunding this second cast is no big deal, just a QoL buff, since Zed skill will go on CD anyway and the damage is unchanged anyway.
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What do you play into Zed? No point in advice without knowing what your champions can realistically do
All he has to do is appear out of nowhere and press R
So it sounds like your issue is rooted more in your map awareness and positioning on the map than zed itself. When you're against anyone with any burst or catch potential, you generally don't want to wonder into areas where they could be alone. This includes pushing out when you don't have vision. It takes some time to get used to, but eventually it'll be second nature.
