Zoe's most basic combo. Shooting the star behind you will give extra distance before launching it again for wave clear or basic poke damage in lane. This can also be done by shooting the start forward and redirecting the star quickly after, to either the sides or slightly forward. If you're in range to auto attack feel free to do so.
E Q Q + Auto:
Another of Zoe's basic combos. Lading the E will give you time to shoot Q backwards and get both the E increase damage and the increased range damage on Q. The following auto will make good use of your passive.
Q R Q + Auto:
Used to gain distance for Q damage and is a quick and easy wave to poke, waveclear, or finish off kills.
R E Q Q + Auto:
Using R to get into melee range use Zoe's E to easily apply your sleep. While they are stunned, line up Q and finish the combo for maximum damage with no return.
E R (backwards) Q Q + Auto:
Another variation of the previous combo, but in a different order. Adds a different style of surprise to the combo, but lacks in E reliability.
Q R E Q + Auto:
Not reliable but plays around the trickster element of Zoe, providing you can land your skill shots.
R F E:
A combo that gives you a lot of range to land your E. Great for engage or picking enemies as you teleport back to your R and out of danger.
Q R E Q: T
his combo is extremely reliant on landing your skill shots and is very quick. With little room for error the combo will not be used in a lot of situations and should be replaced with simpler and more effective combos.
R (Behind a Wall) E:
Allows to cast E at a longer range and catches enemies off guard. Probably my favorite combo and is pretty similar to how high elo Fizz mains use their ult to kill their laners.
Q Q R:
A way to shoot a Q by throwing it behind you and shooting it before R-ing foward to increase the distance, like you were to do a Q-R-Q. (Thanks to https://www.reddit.com/user/Kazistrasz)
*All other combos are most likely not worth noting (not reliable) or are similar variations of the few listed.