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I'm having trouble shaking this answer out of my PHB.
Scenario: I cast a spell that affects a 3x3 area. How many attack rolls do I make? Do I make one per creature in the area (IE, like 4e), or one total attack roll?
PHB cite for answer vastly appreciated.
Area effect spells generally don't involve attack rolls.
This might be why you're having a hard time finding it. 4e has got you used to making attacks against all targets in an AoE; but 5e doesn't work that way, and therefore doesn't tell you to do that anywhere. (It also doesn't say not to, but naturally it can't include every possible negative instruction.)
Individual spells will say so when they require an attack roll. Mostly this is for ranged, single-target effects (though AoEs that can go "wide" from where you wanted them to land could conceivably call for a single attack roll for placement). For the AoE itself, instead of individual attacks made by you, generally the spell will say that the targets caught by the AoE make saving throws to avoid or mitigate the effect.
As a rule of thumb, only one side rolls: either you, or the targets. You'll notice that when attack rolls are called for, targets aren't given saves; when saving throws are called for, you don't also roll to see if you hit.
Generally, area spells do not require you to make an attack, as your spell is not focusing on a particular target or set of targets. Rather, your spell targets a specific point of origin, from which the spell's effects originate in whatever shape is in the spell description. For instance, Fireball deals 8d6 fire damage to everything within a 20ft radius sphere, originating from a target point of origin (in the center of the sphere). Creatures within the Area of Effect(AoE) can make a Dexterity Save to take only half of the damage I roll, rounded down (unless a creature has Evasion, which makes it take half damage on a failed save and no damage on a successful one).
TL;DR You don't roll to attack; the affected creatures roll to get out of the way (or otherwise not be affected by the AoE spell).
P.S. I can't really find anything that specifically says "area spells do not use attack rolls" or anything along those lines. What is true though is that if a spell has the caster make an attack roll of any sort, the spell will say so in its description.
