League of Legends (LoL) Question: How to deal with assassins with an ap mage?

My 4 advice on dealing with assassins:

• Better positioning. Every assassin has its "certain death" range. Make sure to stay out of it. Add Flash's range plus some if you're alone.
  
  
• Buy a mana item or aim better. If you're draining your mana without killing your enemies you should be missing too many skillshots, lacking damage or forgot to buy a Morellonomicon/ Athene's Unholy Grail. Only buy one of those two though.
  
  
• Save your skills for priority targets. Don't burn your CC on the frontline tanks only to have Zed appear from behind while you have your stun on cooldown. If you're afraid of an assassin and can't see him, save your stuns/snares for them.
  
  
• Buy AP items with defensive components. Zhonya's Hourglass versus AD or nuke in general, especially if it's telegraphed ( Zed's ult, Fizz's ult). Abyssal Mask versus AP, mostly if you're melee or short range mage. Athene's Unholy Grail versus AP, should be bought instead of Morellonomicon.

You MIGHT buy one full defensive item, but I would only recommend it if you're fed and melee or short range. If you're behind or play a decently ranged mage your best bet is having a better timing on your CC and knowing how to position properly.

Honestly, it's really helpful to take Exhaust. Depending on your champion, you can itemize against AD burst with Zhonya's Hourglass and/or Rod of Ages.

Don't neglect any core items (e.g. Morello's or something for sustain) just to rush Zhonya's because it's really expensive.

Most AD mids have to poke you down before they can all-in you, so the way you play your lane before you get bursted is really important.

Well, usually your laning phase will suck against an Assassin, so you need to know when and how much CS you want to give up in order not to give them kills. Losing 10 creeps is not such a big deal if they don't get to snowball. Of course you must try to keep up with them, but if you see you are being harassed too much, you need to adapt your playstyle. Also, try to follow them up on roams if you're not behind, since in a 2 v 2 situation it's quite hard for them to do anything if they are even with you.