I saw many Guides for Syndra but the most of them was too squishy (for me). So I want to show you how I play Syndra on my way and I think my guide works well. Perhaps you say "Omg, AP Carry needs to be squishy to do more dmg!" ... Well, I carried most of the games (sure, not all games are all the same). Just try it and leave me a comment with your Score or opinion :)

Azu~

The Pros

+ hard to kill (almost 3k HP and defense)
+ still deals hard Dmg
+ great farmer
+ hard to counter (My Scores said that!)
+ good Teamfighter (multistun with Scatter the Weak)

The Cons

- eats alot of Mana in early Game (a Bluebuff would help much)
- hard focused
- DEAD if Syndra fails her Spells

Why Greater Seal of Ability Power and Greater Glyph of Ability Power?
I also like the flat runes more than the runes per Level. In early game you can hit hard already.
Feed in early game = win at late game :D

Why Greater Quintessence of Movement Speed?
Syndra has a low movement speed (in my eyes ^^)

Boots and 3x Health Potion are the standard opening items and they work good (and you don´t need to sell Doran's Ring)

Try to stay on your lane and farm for Giant's Belt or Blasting Wand. Get it as fast as you can.