This is my 1st ever build on Mobafire. I usually mid with anivia but once Syndra came out I had to snag her. Very high dmg for an AP champ. probably one of the, if not THE highest dmg among them.

Typical 9x [Mark of Insight], 9x [Greater Seal of Replenishment] and 9x [Greater Glyph of Potency]. Also, the 3x [Greater Quintessence of Potency]. Gives her additional AP early game along with mana regen to keep her in the lane for a longer period of time. The magic pen. to add to the early on dmg. could probably swap out the GSR's for Seals of warding for sustainability vs other ap's.

basic masteries for an AP champ. beef the ability power and give her more dmg. along with mana and mana regen plus the buff sustain.

I usually start off with boots and 3x pots. Then I go for the Chalice. Helps mid vs other AP champs. could prob substitute Phil. stone for it to get extra gold and some health regen.

then i get giants belt for extra health early on. Don't usually get rylai's till later though. next is the hextech revolver. gives u some spell vamp to go with some AP. Next i finish rylai's and then go finish boots. u can always do boots earlier but i found the extra health and spell vamp is more crucial. finally i get abyssal scepter followed by a rab's if the game goes on that late. usually abyssal scepter is towards the end and ur team is up big (hopefully)...can also finish athene's unholy grail if u want. not really needed though.

Usually level up 'q' 1st. wait on 'e' till 4 or 5. obviously lvl up 'r' at 6, 11, and 18. obviously gives benefits to fully upgraded skills so that extra dmg on 'q' helps a lot. 'w' is next to max and lastly 'e'. though her 'q' requires a lot of mana late game it does a lot of her damage too.

Ignite and Flash are crucial in my view. that extra dmg from ignite helps finish your foes while you have some escape with flash. could subsitute tele for ignite since you're probably mid.

Pro:

High Ability Dmg
Nice slows with her 'w'
very low cooldown on 'q' and 'r' early on
'w' and 'e' get lower cooldowns late game

Con:

very squishy
stun is hard to hit
extremely slow champ. (mobile champs like ahri would shred you)

Stay back and harrass champs in team fights. once you have a few orbs out (2-3) then use your ult on the AD carry or AP champ. usually both are squishy enough you can obliterate them.

Can easily sustain in mid vs most AP champs. high dmg can cause high health champs like mord to stay back. could easily press your lane and steal the advantage. even mobile AP champs like ahri still have to watch out lest you lay a trap that destroys them. especially if your ult is up.

waiting on the last hit and if multiple minions are low feel free to use your 'q' to get the extra gold. late game when you get it maxed you can pretty much destroy hordes of minions with it and get tons of gold that way to finish the build.

Glad you guys got this far. I'm sure it was a boring build guide, since it was my 1st, but I hope that everyone got a taste of my view of Syndra and all her phenomenal cosmic powers!