There are several instances in the books from which we can glean some information about the forest's size. In Philosopher's Stone they are already well into the forest when Harry, Malfoy, and Fang split off from Hagrid, Hermione, and Neville, and we are told that they walked on for almost a half hour:
So Harry set off into the heart of the forest with Malfoy and fang. They walked for nearly half an hour, deeper and deeper into the forest, until the path became almost impossible to follow because the trees were so thick.
In Chamber of Secrets we have another description of time spent walking in the forest:
So, with Fang scampering around them, sniffing tree roots and leaves, they entered the forest. By the glow of Harry's wand, they followed the steady trickle of spiders moving along the path. They walked behind them for about twenty minutes, not speaking, listening hard for noises other than breaking twigs and rustlings leaves.
And shortly thereafter:
They walked on for what seemed like at least half an hour, their robes snagging on low-slung branches and brambles.
So not counting the time between the twenty minutes and the half hour, it took at least ~50 minutes to reach Aragog's lair.
On the way back from Aragog, they traveled in Mr. Weasley's car, and we have the following description:
They smashed their way through the undergrowth, Fang howling loudly in the back seat, and Harry saw the side mirror snap off as they squeezed past a large oak. After ten noisy, rocky minutes, the trees thinned, and Harry could again see patches of sky.
In Goblet of Fire Hagrid showed Harry the dragons. We get the following description of the walk to the area where the dragons were kept:
But then — when they had walked so far around the perimeter of the forest that the castle and the lake were out of sight — Harry heard something. Men were shouting up ahead... then came a deafening, earsplitting roar....
We can put a loose time estimate on this because we know that Harry was supposed to meet Hagrid at midnight:
Hagrid now bent down on the pretext of reading the S.P.E.W. notebook as well, and said in a whisper so low that only Harry could hear it, "Harry, meet me tonight at midnight at me cabin. Wear that cloak."
And we know that Harry was supposed to meet Sirius at 1:00 in the morning:
Can you ensure that you are alone by the fire in Gryffindor Tower at one o'clock in the morning on the 22nd of November?
And we know that almost immediately after he got back, Sirius appeared in the fire:
Harry pulled off the Invisibility Cloak and threw himself into an armchair in front of the fire. The room was in semidarkness; the flames were the only source of light. Nearby, on a table, the Support Cedric Diggory! badges the Creeveys had been trying to improve were glinting in the firelight. They now read POTTER REALLY STINKS. Harry looked back into the flames, and jumped.
Thus, it took about an hour to walk around the perimeter of the forest, dawdle for a few minutes with the dragons, and get back to Gryffindor Tower. We can get an even more precise estimate when we note that shortly after Harry started heading back we have the following description:
Harry sped up, skirting the edge of the forest; he had just under fifteen minutes to get back to the fireside and talk to Sirius.
This tells us that a large majority of the hour was spent on the walk around the perimeter of the forest to get to the dragons.
In Deathly Hallows, Voldemort announces that Harry has one hour to appear in the forest:
"I speak now, Harry Potter, directly to you. You have permitted your friends to die for you rather than face me yourself. I shall wait for one hour in the Forbidden Forest. If, at the end of that hour, you have not come to me, have not given yourself up, then battle recommences. This time, I shall enter the fray myself, Harry Potter, and I shall find you, and I shall punish every last man, woman, and child who has tried to conceal you from me. One hour."
At this point Harry went from the Shrieking Shack to Dumbledore's office, watched Snape's memories, and then headed into the forest. We know that he made it to where Yaxley was patrolling at just about the end of the hour:
Yaxley looked down at his watch.
"Time's nearly up. Potter's had his hour. He's not coming."
Then they walk for a few minutes until they reach Voldemort's base, in what used to be Aragog's lair:
They had traveled on mere minutes when Harry saw light ahead, and Yaxley and Dolohov stepped out into a clearing that Harry knew had been the place where the monstrous Aragog had once lived.
We also know that when Harry finished watching the memories, he still had a little more than a half hour left:
He looked down at the battered gold watch he had received on his seventeenth birthday. Nearly half of the hour allotted by Voldemort for his surrender had elapsed.
Thus, it took a bit more than a half hour to get from Dumbledore's office to Aragog's lair.
(This perhaps contradicts the time it took in Chamber of Secrets, but one could suggest that Harry was in more of a rush in Deathly Hallows, or his stride was much longer, or that in Chamber of Secrets it took longer than it should have because they had to constantly check where the spiders were going.)