1.) Your lvl 2/3 is very powerful, make use of it! Especially if you reach lvl 2 before your enemy and skill W, you can get easy first blood.
Just walk up to your enemy (care for minion wave tho) and use ignite... The movement speed will make it hard for the enemy to escape.
If you can land Q use it. Enemy now can flash away or fight back with ignite so basically you have 2 flashes and/or 2 ignites and he is still lvl 1, so you should win.
Same with lvl 3 spike (bubble), it's just important to have minion advantage and exp advantage early on, but even without you can force fights.
But! some matchups you should play a bit more passive until you got some items.
2.) Roam a lot, especially botlane. Your bubble and W are perfect for this. Botlane can give you like 4 summoners and they are squishy.
3.) When playing Zoe, the enemy jungler can be free kills, depending on the champion. If they have squishy jungler like Twitch/Nidalee etc. and you see them in the jungle with 1 lvl below you, just use bubble and kill them. They don't expect it.
Other than that, just play her a few times and get a better feeling for her Q and distance. You will automatically play better with time.
A small tip: You can swap your summoner/item from w if you see a better summoner/item on the ground by right clicking on it.
Another small tip: Playing her with Hexflash is funny, since it always procs your W because it technically is a summoner skill. It also helps roaming (going over walls)
My last small tip: If you have a summoner spell like heal or flash and the time to use it comes to an end or you didn't go back for a long time, just go back to base. Buy items and use them on the way back to the lane. This way you are faster and don't miss minions.
. after thats its either 
or 
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against a 
or 
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