If we're not getting into savage openers and all that stuff, your basics are as follows.

Single target:
Jolt -> Verthunder -> Jolt -> Veraero (or swapped if you want, doesn't matter). If you get a Verfire or Verstone ready proc, cast one of those instead of Jolt. They do more damage and give you more total black/white mana than Jolt does, plus they have the same cast time. Your basic goal is to avoid casting Jolt as much as possible. If you have Accelerate up, it acts as a combo Swiftcast and proc guarantee for Verthunder and Veraero.

Ideally, you want to be rotating in one of two ways given perfect proc luck: Verstone -> Veraero -> Verfire -> Verthunder, or Verstone -> Verthunder -> Verfire -> Veraero. This sounds confusing at first, but if you arrange your hotbar so that the proc spells are situated just above the slow spells that trigger them, you'll see it looks like this:

1 3
2 4

or
1 3
4 2


Which one of these patterns you end up following will mostly depend on how your procs are lined up. Your secondary goal (after trying to never cast Jolt if you can help it) is not wasting procs. If you're casting Verfire, and you see you already have a Verstone ready, then your next spell should be Verthunder. This probably sounds like a lot of information, but just remember- this is all in service of making sure you cast Jolt as few times as possible. The best thing you can do is try to keep both procs lit as often as you can. When you get to at least 50/50 black and white mana, you can do your Riposte -> Zwerchau -> Redoublement combo, since they're fast GCDs and end up doing more damage than your spells in their enchanted form. As you level up, this melee combo will gain more finishers after it, and these finishers will auto-replace abilities on your hotbar so you don't even need to worry about managing them.

For AOE:
Much easier. You want to go back and forth with Verthunder 2 -> Scatter -> Veraero 2 -> Scatter. Scatter later upgrades to Impact just in case you see someone refer to the spell as "Impact", but the rotation remains the same. When you get to 60/60 black/white mana, you can use Moulinet three times for the same flow as your single-target finisher. Something to note is that your two target rotation is where things get a little wonky. Technically the highest potency on two targets is Jolt -> Scatter, because Jolt does more total potency than Verthunder/aero 2 do to two targets. Nobody is going to fault you for just using the base rotation, but that's something to keep in mind for later.

Other notes:

Keep Fleche and Contre Sixte on cooldown. They're free damage, and it's basically never a gain to hold onto them, single target or AOE. Other abilities you get later on are situational party assistance skills or upgrades to your basic flow. Manafication and Embolden should be used together as often as you can, but nobody's going to care if you mess those up. As you get used to the back and forth white/black flow of your basic spells, you can start doing things like weaving Swiftcast to try to force a proc instead of casting Jolt, or using Accelerate/Swiftcast for movement.