Been playing Zoe since I first started the game(Around summer of 2018). I played the champ from levels 12-130ish then just got bored of her and stopped. She has very high poke and burst damage even without items and is one of the best level 3 all in champs in the game. You can run a wide variety of runes and items with her which is nice. The main thing is just getting good at landing your q's. Besides that she is a pretty easy champ with high damage. I'd recommend roaming and helping other lanes the most if you are on top side of the map(I think it is red team?). That way it will be easier to set up sleeps on bot and top lane.

I stream occasionally, and when I do it's league. If you want to see me play Zoe just ask in chat and I will.
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Grasp is my personal favorite to run on Zoe. It works well in mid and top lane, especially against a melee champ. Try to use it as often as possible(Should be able to use it around 35 times in the first 10 mins against aggressive melee champs), and when you do ONLY auto-attack them, if you all in then they will stay back and not risk getting damaged. See Grasp item and rune pages for more info.

Klepto can work on Zoe if you play it right. It will truly only work if you are going against a melee champ that doesn't have any ranged abilities to cs with. Just make sure that the wave is pushing against you constantly so that way they have to stepup to cs and can't just sit back. The best champ to use klepto against is probably yasuo, since he doesn't have to worry about taking too much damage due to his passive. For more info check the Inspiration rune page on this guide.

Press the attack isn't the greatest rune to rune on Zoe. If you do, proc press the attack before hitting your q/hitting the enemy champ while they are slept. You still build ap. This rune also isn't bad for poking laners, as procing PTA will deal damage to them at the end(Pretty much a worse electrocute). PTA does have the potential though to deal more damage then other runes as long as you proc it before going all in.