First: I apologize this isn't video, but I don't currently have a computer good enough to record/process video, and the PC방 computers don't have that kind of software on them.
I see a lot of people still confused about HOW Zoe's skills function exactly. There won't be many "tips and tricks" here, it's just a rundown of the actual mechanics behind her abilities.
Let's start with her R. Somehow, her ult is the simplest skill.
By now, you probably know that her R opens a portal under you and at your destination, and blinks you to the destination portal for one second before returning you. During this time you can use any ability, summoner, item active, etc. that you want and auto-attack (only once unless you build AS). No matter where you end (even if you double- or triple-flash), you will go back to your starting location.
If you are hit by any form of CC or displacement, you will still be moved back to the original portal. This includes if you get caught by a Blitzcrank hook. There are a very few exceptions involving abilities where you get physically anchored to the other champion (Skarner ult for example) that you are not immune to.
The other thing I want to make sure people know is that this works EXACTLY like other blinks, Flash, and wards in that you can use it to get over very large walls. You can use this to make enemies accidentally screw themselves by dumping them in random places if they follow you (Lee Sin, Master Yi).
Now for her Q
If you're reading this, I assume you know that her Q is a skill shot that can be re-cast within a second to redirect it. One thing people do not realize is that you can re-cast it early to get different angles or avoid it hitting a jungle monster before you re-cast it).
The big part people are discussing/debating is how to use this in combination with her ult. The correct answer in terms of damage potential is Q-Q-R, though there are times (especially where vision is needed) that Q-R-Q can be used. Let me explain how Q-Q-R provides the most damage.
Here's standing at max range and throwing it from one side of the circle to the other.
Using Q/R/Q let's you quickly jump forward before you launch your Q, but it locks you in place. This is one problem with this approach. Here's the range you can get. The Q started a little bit behind tower.
What many people don't realize is that the Q's range is dynamic while it is in motion. That is, if you throw it behind you, and then throw it forward, you can walk forward with it to extend its range. It will travel until it hits the max-range circle around Zoe. You can use Q/Q/walk to get the same range as Q/R/Q.
If you incorporate this with Q/Q/R, you can actually stand BEHIND mid tier 1 turret and hit someone in the middle of the lane. To achieve this range, you need to Q behind you, start walking forward, then throw your Q at the enemy at the last moment you can, and continue walking forward. Again, right before the Q will run out, you ult forward again. If you compare to the first picture about her Q, you can see this gets you more than 150% of the damage from her max-range-to-max-range.
Her E actually requires MORE geometry.
Her E is naturally a medium-ranged skill shot. The exact way it works over walls is different than normall skill shots.. Normally, if you are out of range, the skill shot goes until its max range and stops. However, her E is completely different. Once it hits a wall, the game "pauses" its range, and continues it through the wall. When it passes through the other side of the wall, it resumes. Unlike every other skill shot, her E becomes even longer over walls.
Her E will only extend over a single wall at a time, and it will stop before the next. Even if there is extra range not used yet for her E, it will not exit a wall, pass through the next, and then go further.
The EXACT way the game calculates the range goes down to the size and width of the bubble. Important to this, the distance between turrets and walls is smaller than the width of the projectile. This also applies to Nexus turrets. If you aim the E over a wall into a turret, the gap between them is narrow enough that the E never actually leaves terrain, so the game doesn't count this as a gap. You can stand behind a wall, and hit someone on the other side of the lane if you aim well.
This also applies to curved walls. As long as the entire projectile doesn't leave a wall, you can fire it the entire way down a wall. This is especially important to your base. The little gates that only one team can use count as a wall, not a gap (including your own). You can stand in the mid lane entrance and hit someone at the bot lane entrance.
When you are fighting front to back, you can use this to reach farther into the fight. Combined with her ult, you can quickly access backline targets that you otherwise have no business attacking.
Another important note about her E is that you can still see it working in fog of war. Like many skill shots, you get visual confirmation when the skill makes contact. But, it's equally important to know that you also get to see their location once they fall asleep. You can use this to check fog of war, and also to set up abilities for your team when you know the enemy team is there.
Edit: I forgot to mention that her E will still hit anyone that is inside a wall as it goes through. You can use this to fuck on Kayn and Bard.
Lastly, her W is the coolest part
I'm going to assume you know about picking up summoner/item active bubbles and that you have to use one before picking up the next. Edit: I have been informed you can walk onto a new one and right-click to pick it up. There is no cooldown to her W-version of summoners, so if you're trying to clean up the end of a messy team fight, you can flash every time you reach a new flash bubble and get around the area much faster than anyone else.
Riot actually added a very nice quality-of-life feature to the W. If you have picked up an extra version of a summoner spell or an extra version of an item active that you actually have, pressing the button for your summoner (D/F) or item (1-7) will use her W first before consuming your actual cooldown. This does not, however, protect you from using both if you're a button-spammer.
Lastly, her little bubbles work similarly to Ahri's W. They fire one-at-a-time over roughly a full second. They will fire at the last target you attacked if it is in range.. If you haven't attacked anything that's in range, they will automatically shoot at the nearest target. Unlike Foxfire, they DO NOT prefer champions.
Okay, I think that just about covers everything.
Sorry there's no video, but unfortunately my real machine that can do video is another country. If there's anything I missed that you want to know, comment it and I'll try to find out and update you.