Hey, this is IceyEmerald/LoveofIceyFlames, and I'm presenting a Syndra guide. I will not say I'm pro, actually I'm very much nub, but I've been rationalizing this build since Syndra came out. Hopefully, you will find it somewhat useful. Also any comments on how to improve this build (such as more detail in certain areas, or how to add pictures because I can not figure it out for the life of me)

Pros:
Great burst
Has a slow and stun
Pretty fun if you like throwing your opponent's minions at them

Cons:
Squishy
Mana hungry
Difficult to master

Greater Mark of Insight: Magic Penetration on an AP Caster, kind of seemed like it was best choice.

Greater Seal of Replenishment: I chose this because since the majority of Syndra's skills are skill shots, spamming happens a lot and that makes us run out of mana much faster then the other laner. These runes tend to help keep up.

Greater Glyph of Force: I find more power viable in most cases, you could go for the flat ap glyphs but these out scale those quickly. If you need more survivability I suggest getting magic resist glyphs instead.

Greater Quintessence of Potency: Flat AP quintessences give us a tad bit of early game power vs getting scaling quintessences. If you went for flat glyphs I suggest getting scaling quintessences instead.

I went with 21/0/9 masteries because Executioner goes great with a Level 5 Dark Sphere, and added utility over defensive because for 1, the mana regen helps stay in your lane longer and plus the longer buff durations helps a lot, though it can go unnoticed in a game where you are doing horrible.

I am still working on this part, if you have any item suggestions please put them and I will test myself and add if they work well.

While leveling your sequence (if your following this build) should be R>Q>W>E, most champions I've seen follow this, Syndra is no exception.

As far as combos go I use:

Q>E>W>Q>R
This sets a Dark Sphere down and then stuns, your W then slows because the stun doesn't last very long, while they are slowed, another Dark sphere should be placed, and whether it hit or not doesn't matter because directly after you should ult so the first dark sphere doesn't fade. This gets a great deal of damage in so long as you are positioned correctly to hit them all.

R>E>Q>W>Q
This starts with your ult so you can place all your Dark Spheres then push them out to stun anyone around (this is assuming you are in a team fight). Then burst the damage dealer with Q; if he dies good, if he doesn't use W to hit him again with a stronger burst; is he dead? If yes, run because you probably took a deal of damage. If no, check your hp and his, if you can survive long enough to secure the kill then chase, if not, fall back.

Q>E>W
If someone is minion/turret diving you and you want to be safe, place a Dark Sphere, use E to stun them under fire, then use W to hurl your ball to get some extra damage in. This may be enough to send them back to their base, if not kill them early game.

Q>E
I use this typically to run, place a Dark Sphere behind me and immediately use E to stun my chaser. If you are running you don't have time to think about positioning.