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I was sitting here, thinking to myself, "How does one hit multiple enemies that are behind total cover and low to the ground?"

Fireball states that it targets "a point you choose within range", and hits everything in a 20-foot radius. So if I cast it 15 feet in the air so as to hit some goblins or whatnot that are crouching behind a short wall, or thick brush or something... would it still hit them even though I cannot see them?

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Yes

Well, first of all, the fireball spell description states:

The fire spreads around corners.

And Jeremy Crawford has clarified on Twitter that:

Your cover is foiled if an effect spreads around it and reaches you.

In addition, regarding spell targeting (and the targeting of Fireball in particular), Crawford has explained that this is possible:

Can a wiz target empty air with fireball or does it need to hit something solid to detonate? Are air bursts legal?

Fireball requires you to choose its point of origin. Its text doesn't require that point to be on an object. A point in space is fine.

How precisely can a wizard dictate that? Can he choose to cast it at a point exactly 23.5 feet away?

As precisely as the DM allows.

In general, you don't need a line of sight/effect from you to every point within the area of effect of a spell or ability unless it says otherwise. For area-of-effect spells, you simply need a clear path to the point of origin that you are targeting. After that point, the spell description describes how the effect is applied (and whether the spell spreads around cover).

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Absolutely

The rules require you to have a clear line of sight to your target (in this case, the point of origin of the spell):

A Clear Path To The Target: To target something, you must have a clear path to it, so it can’t be behind total cover. (PHB, p. 204, or here in the Basic Rules)

There are also rules that (usually) require a thing to have a clear path to the point of origin for the thing to be in the area of effect:

A spell’s effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn’t included in the spell’s area. To block one of these imaginary lines, an obstruction must provide total cover, as explained in chapter 9. (PHB p. 204, or here in the Basic Rules)

But you do not need a "clear path" from you to a creature for it to be in the area of effect of one of your spells.

Note: Since Fireball states that "The fire spreads around corners" (PHB, p. 242), note that fireball would often affect creatures "crouching behind a short wall" even if the creatures were on the opposite side of the wall from the point of origin, and the point of origin was at ground level. But for other spells which do not go around corners (such as Shatter), this remains a viable and valuable tactic.

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    \$\begingroup\$ By the way, I am aware that technically any creature in a fireball's area of effect is also one of its "targets" (since the spell defines it as such). But in the case of "a clear path to the target" on PHB page 204 refers to the point of origin, not the creatures being damaged. \$\endgroup\$ – Gandalfmeansme Jun 3 '18 at 6:36

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