It is recommended to get one of your spells to rank 5 as quickly as possible to benefit from its Transcendent bonus.
Maxing Dark Sphere first is highly recommended. This will increase the damage vs champions, while the other Transcendent bonuses offer improved utility but no extra damage.
It is also recommended that smart casting is used on all of Syndra's abilities except her ultimate. This allows for seamless transition between her abilities and faster combos, which is critical in team fights.
However, while Dark Sphere and Scatter the Weak are musts for smart casting, you may not want to smartcast Force of Will as you could end up grabbing a minion instead of a sphere or grabbing the wrong sphere. This problem disappears as you get used to Syndra.
To get out 4 bonus spheres (the maximum possible) you need more than 30% cooldown reduction and you can do this by using the following combo: Q, Q, W (targeting the first sphere), Q, Q, followed immediately by Unleashed Power. However, the delay on her ultimate and the increased micromanagement requires a higher level of skill on an already difficult champion. For most players, it may be more efficient to try using Q and E, Q again and W on the first dark sphere, and then use Unleashed Power - this sacrifices one or two dark spheres on her ultimate for a quicker, more reliable combo.
Four sphere combo is mostly used to kill a very tanky champion, like a fighter.
Two sphere (assuming you actually hit the damage of the sphere summoning itself) is usually enough to smash a squishy target (Syndra decimates squishies) like a Marksmen or Mage.
One or no sphere is only used if you have everything else on cooldown and need to kill someone immediately, the damage is actually quite respectable with only one bonus sphere.
If you notice your opponent is easily avoiding all your Dark Sphere try to become more conservative about it, the low cooldown makes it tempting to use continuously, but pushes the lane if you hit minions (and invites junglers) and drains your mana quickly at higher ranks.
Dark Sphere has no channel upon cast, which means you can cast it without interrupting your movement. Take this into consideration when playing Syndra, since it allows you to kite and chase enemy champions easily.
During laning, keep Syndra always on the move, only stopping to last hit or kill someone. This way Syndra will be more safe from skillshots and delayed abilities and she will be free to poke with Dark Sphere while still moving.
To maximize your chances of hitting the enemy champion with Dark Spheres, use it right when they last-hit.
After you hit an enemy champion with Force of Will, follow up with Dark Sphere; they'll be slowed and have a hard time avoiding it. If you are confident enough in your own aiming, casting Dark Sphere right after Force of Will will cause them to hit at the same time; this can save a few seconds if you are considering a combo for Unleashed Power.
When being chased in the jungle, use Force of Will on a nearby neutral monster to slow the enemy champion.
Thin choke points like most of the jungle will make it easier to use Scatter the Weak when an opponent gets too close.
Scatter the Weak will still stun a champion if they get between a Dark Sphere and yourself, if they are in-line with the abilities knockback. Note that the stun occurs when the sphere and the enemy collide, therefore you do get a fraction of a second's length longer on your knockback-stun cc chain if you hit a nearby enemy into a farther away sphere.
When fleeing, creating a Dark Sphere and/or using Force of Will won't halt or slow your movement at all, making these good options for deterring chase or making it impossible to catch up to you, particularly if you have Rylai’s. Scatter the Weak's cast animation may allow pursuers to gain ground necessary to use a targeted ability on you, therefore you should consider if this might be the case before using it to secure an escape.
Try to stay back in teamfights since Syndra is pretty fragile.
Syndra's damage output is reliant on a high CDR build - it will provide stronger harass with Q and W combos, and being able to maintain more dark spheres on the battlefield will potentially increase the damage on Unleashed Power.
She is extremely mana hungry. Athene's Unholy Grail provides every stat she needs; AP, CDR, and mana regen.
The passive on Rylai's Crystal Scepter synergizes with all of her spells to varying degrees; however the bonus mana on Rod of Ages will help with Syndra's high mana costs and may be a preferable option depending on your runes and masteries.
Building a Deathfire Grasp will help provide Syndra with more AP and CDR, as well as its active effect will help with her damage output and improve her burst.
It has been debated that Manamune is a better purchase on Syndra due to the Muramana active, which triggers per sphere during Unleashed Power. With only Muramana for mana, the bonus damage per sphere at full mana is between 93-129 (level 6-18). This is the single most damage attainable from only a single item, and is the equivalent of having 465-645 bonus ability power. This is 279-387 bonus damage with only the minimum 3 spheres.
With no reliable escape tool she is also easily ganked and weak against champions with gap closers and crowd controls.
When ganking her split up so she can't use Force of Will and Scatter the Weak to disable both you and your ally. If she manages to stun she will also easily get to slow you, and will likely escape if both you and your ally are affected by this.
If Syndra keeps creating Dark Spheres in a situation where she would be better off doing something else (like re-positioning or knocking back enemies), then she is likely preparing to use her ultimate.
But beware when she has 3-4 Dark Sphere on the terrain during teamfights, because she can then deal massive damage with Unleashed Power (up to 1260+140% AP), followed by Scatter the Weak to instantly kill a team member and stun the whole team if you're not spread out enough.
Syndra is a bursty mage, try to focus her down first if you are having problems with her damage.
In late game she can be very powerful with her spammable nuke. Try to deny her farming early game to cut down on her damage potential later on.
Be wary when dueling in a 1v1 with Syndra. If her ultimate Unleashed Power is available she can instantly burst you down before you are able to kill her.
The Scatter the Weak and Dark Sphere stun combo can be very hard to land if enemy is too close to her, meaning bursty melee assassin can kill her with ease.
If using this method, beware her ultimate Unleashed Power since it has pretty short range, meaning she might use it on you, being the closest person. Try this plan when her ultimate goes on cooldown. (Warning: at rank 3 her ultimate's range is increased by 75)