In Harry Potter book 1, Harry, Ron and Hermione go down into the trap door in order to get the Sorcerer's Stone before Quirrell is able to do so. However, they seem to know already that this is the day when Quirrell is planning on stealing it.
How did they know that this was to happen on that particular day?
They suspected that Snape (Quirell) was attempting to steal the Stone that day because of a few things.
They had just found out that Hagrid had leaked the secrets about how to get past Fluffy:
"Let's see... yeah, then he said he had the dragon egg an' we could play cards fer it if I wanted...but he had ter be sure I could handle it, he didn' want it ter go ter any old home...So I told him, after Fluffy, a dragon would be easy..."
"And did he -- did he seem interested in Fluffy?" Harry asked, try ing to keep his voice calm.
"Well -- yeah -- how many three-headed dogs d'yeh meet, even around Hogwarts? So I told him, Fluffy's a piece o' cake if yeh know how to calm him down, jus' play him a bit o' music an' he'll go straight off ter sleep --"
Hagrid suddenly looked horrified.
Upon trying to warn Dumbledore, they found he had left the castle on an emergency meeting (at the Ministry).
"Professor Dumbledore left ten minutes ago," she said coldly. "He received an urgent owl from the Ministry of Magic and flew off for London at once."
"He's gone?" said Harry frantically. "Now?"
"Professor Dumbledore is a very great wizard, Potter, he has many demands on his time."
"But this is important."
"Something you have to say is more important than the Ministry of Magic, Potter?"
"Look," said Harry, throwing caution to the winds, "Professor - it's about the Sorcerer's Stone-"
Putting these two things together they concluded that the robbery would be happening as soon as possible, so they attempted to steal the Stone first.
It appears, though it isn't explicit, that Dumbledore received a fake note to go to the Ministry.
"I see you are not to be distracted. Very well, the Stone. Professor Quirrell did not manage to take it from you. I arrived in time to prevent that, although you were doing very well on your own, I must say."
"You got there? You got Hermione's owl?"
"We must have crossed in midair. No sooner had I reached London than it became clear to me that the place I should be was the one I had just left. I arrived just in time to pull Quirrell off you."
A lucky coincidence.
When Harry et al. are talking to Hagrid about the night he bought Norbert, Hagrid explains that he met a shady character who was interested in Fluffy, and got Hagrid to spill the beans:
“Well - yeah - how many three-headed dogs d'yeh meet, even around Hogwarts? So I told him, Fluffy's a piece o'cake if yeh know how to calm him down, jus' play him a bit o'music an he'll go straight off ter sleep-”
They (correctly) surmise that this is somebody trying to sweet-talk Hagrid, and work out how to get past Fluffy. They take this information to Professor McGonagall, who tells them that Dumbledore has just left for the Ministry of Magic.
They guess that this isn't an accident; plans are afoot:
“It's tonight,” said Harry, once he was sure Professor McGonagall was out of earshot. “Snape's going through the trapdoor tonight. He's found out everything he needs, and now he's got Dumbledore out of the way. He sent that note, I bet the Ministry of Magic will get a real shock when Dumbledore turns up.”
I don't think it's clear whether this was actually a fake note (Dumbledore isn't explicit about this), but it gets their attention.
This is a very lucky piece of plot coincidence. It's been a while since Hagrid got rid of Norbert, and even longer since he would have seen Quirrell in the pub. If they'd gone to Dumbledore just a day earlier, they'd never have known he was out of the castle and that somebody might be making an attempt on the trapdoor.
