TBH the only thing I don't like about Ahri is her W.
If Ahri is ahead, 1 q hitting twice will clear caster minions. If you aren't ahead, prep them by autoing them twice. Ahri can clear waves faster than more assassins because she has a foot in the mage camp, so fast pushing and roaming works well on her. If your opponent roams and you don't want to follow (say it's Fizz), you can easily push the wave into his turret and start taking it while he's trolling your teammates.
For mana, try to use only 1 Q per wave unless you are fast pushing. Don't toss a charm unless you can get a lot out of it like forcing the other guy to burn a flash or recall after the trade. Use your autos for harass as much as possible.
You can also get items to help out:
- 60 mana per minute but it can't be upgraded
- typical rush item
- not great on ahri, she spikes mid-game and this thing takes forever to charge.
- you never have to worry about mana again and it gives a ton of AP, but like RoA the timing is bad for ahri.
- ADC ahri could take this first
Basically you need to work on your last hitting and get ludens ASAP. Try to avoid RoA or Archangels on her because in my experiments, they make her weaker at the time she should be winning lanes. Frankly riot doesn't want games lasting too long anyways.