Be careful when going for short trades with Qiyana as she prefers them over long extended ones.
When Qiyana has her River Element (the blue one), do not overextend or play super aggressively. There is probably a reason she has picked this up and her Jungler may be nearby. Play safer when she holds this Element.
Pre-6, Qiyana will constantly push the minion wave with her Q. Stand outside of the minion wave at all times so she is unable to push and poke at the same time. But, do not stand near a wall so she cannot Ult R you into it.
Qiyana’s team fight presence is huge thanks to her Ultimate R. Spread out and do not fight in choke points like in the jungle or under a tower to reduce her usefulness.
When no team fights are occurring, Qiyana will split push. You can use this as an opportunity to engage on her team when she is unable to impact the fight. Keep an eye on her though and be prepared to recall if she is getting close to your tower.
Burst and CC are your best friends in a team fight. As soon as she engages, try to lock her down with CC and burst her down so she is unable to dish out tons of damage and kill your teammates.
The level 6 power spike for Qiyana is pretty strong because it gives her a game-changing Ultimate R that can be used in plenty of ways. Be careful and do not position near a Tower or wall as she may look to R you into it.
Once Qiyana has her first item completed, she will look to trade more aggressively as she will have extra cooldown reduction and damage. Be careful and do not go for short trades as she favours them.
Qiyana truly shines in the mid-game as her Ultimate R is a great team fighting tool. Unlike many assassins, Qiyana actually favours team fighting.