Spells like fog cloud (PHB p. 243) and darkness (PHB p. 230) create areas of heavy obscurement. Because the point of these spells is mostly to obscure vision, ordinarily (at least in my experience) they are only cast in areas that are not heavily obscured already. For example, unless you're facing an enemy that can see in the dark (via darkvision, blindsight, etc.), there is rarely reason to cast fog cloud in an area that is already completely dark.
As a result, creatures caught in one of these spells usually start out being able to see their surroundings before the spell takes effect. A party of PCs marching across a battlefield in broad daylight will have had at least a glimpse of the terrain before that fog cloud hits them and renders them effectively blinded, at least for purposes of seeing "something obscured by it." (See PHB p. 183 and this errata.)
This has raised questions at our table. The DM draws out a basic encounter map, the players place their minis, etc. — and then one of these spells drops, reducing visibility to zero. The quandary is: Can the PCs respond by moving outside the bounds of the visibility-reducing spell? If so, how? How would they even know where to move?
Clearly the players know what is on the map. And their characters might be able to work with their memory of what terrain features are where, based on what they were able to see prior to the spell taking effect. ("OK, I think the well is over here, and there was a copse of trees somewhere over there…") But, being effectively blinded, are the characters not then unable to determine where the area affected by the spell begins and ends?
This quandary is especially easily observed in — though hardly limited to — play on a grid, where any given spell will routinely affect this 5-foot square but not that 5-foot square right next to it. If I'm effectively blinded because I'm standing in a square covered by fog cloud, can I see that the square next to me is outside the spell's area? Or am I forced to wander around blindly, guessing at where the spell's borders are?
(Bonus round: the party's paladin, stuck in the fog cloud, arbitrarily chooses a path of movement he thinks will take him outside the area, but that in fact runs him straight into the square of the party's rogue, who has used the reduced visibility to hide. Even if the paladin doesn't collide with the rogue, moving through the rogue's square is difficult terrain, see PHB p. 190, which costs the paladin the one extra square of movement that would have actually taken him outside the area.)
That has been the ruling at the table so far: being unable to see in front of you means the only way to know where to move to escape the affected area is by trial and error.
My worry is that this ruling, in effect, cranks up every visibility-reducing spell into a combination of itself and confusion, PHB p. 224-225, in that characters have no choice but to move in random directions in the hope of a lucky escape. Lest that seem like an idle worry, consider spells like stinking cloud, hunger of Hadar, or cloudkill, which not only obscure vision but also actively hamper or harm affected creatures every round they remain in the area. If characters have no way to know where the area is (and isn't), they are much more likely to get stuck in it, being affected round after round.
Bonus points for a rules-as-written answer, but any persuasively reasoned answer is acceptable.
Probably related: Does this errata allow vision out of an area of Darkness?
Best Answer
Going by parts
1. Knowing where the spell starts
As from firechant's answer, the characters can be assumed to know where the spell started, assuming they saw the spell being cast.
2. Knowing where the spell ends
You can't see that the square next to you is outside the spell's area - you are blinded, you can't see at all, period. But, if you have knowledge of the spell (which could be an Arcana check, or an instant pass if you have the spell yourself - it's up to the DM), and knowing where the spell started (check Section 1), you should know the area affected by that spell. If you don't know the spell, your character can only guess - obviously a not-dumb guess would be that going towards the point of origin doesn't help, instead you should probably move away from it, even if you don't know how much you should move. By that logic, the next quoted statement seems too harsh.
As I said, there is a smart "trial" and a not-that-smart "trial". You know, at least, where the spell started.