Give RDM Water and Blizzard already!

[Archwizard]

So I just unlocked this job and everyone says it's super easy but I just don't get it. Can someone please explain to me like I'm an idiot, because I am one, how this job works at level 50?

As TankHunter explained, Dualcast is not a proc; it will always activate off of any non-instant spell you cast regardless of cast time, and make your next spell instant regardless of cast time if it wasn't instant already. (So it won't make two spells instant in a row, but it will go cast->instant->cast->instant, etc.)
This means you could theoretically cast a spell with a short cast time to gain Dualcast, then burn that on a spell with an otherwise 8-second cast such that the latter becomes instant, just like using Swiftcast.

In the simplest manner possible though:

You've got three main types of attacks: Shortcasts, Longcasts, and Melee.

Longcasts are strong spells but have a cast time longer than your 2.5-second global cooldown, like Verthunder, Veraero and (in AoE) Scatter.

Shortcasts are non-instant spells with 2-second cast times that are on the weaker side, like Jolt, Verfire, Verstone and (in AoE) "Ver- II" spells. Generally you want to use Verfire/stone over Jolt any time they're available since they're significantly stronger, but they only proc from your Longcasts, so you'll usually be using Jolt as a starter.

Like you've clued into, the goal is for you to use the Shortcasts to activate your Dualcast trait, and then burn Dualcast to instantly fire off a Longcast spell in quick succession. "Jolt-> insta-Verthunder-> Jolt-> insta-Veraero" is a basic form.
Weave your off-GCD skills (like Fleche and Acceleration) after your instant casts for bonus damage, so that you keep them on cooldown.

Alternate between spells that will generate different Mana types in your Balance Gauge so that you build them at a near-even rate, and once you have at least 80 of each type of Mana at once you can use your melee combo, which is the most burst damage you'll do.
You'll probably also want to play with using Corps-a-corps and Displacement to transition into and out of your melee combo, respectively.