Keep following the main story line for this trophy.
*** Spoiler - click to reveal ***The Throat of the World
You will first have to talk to Arngeir of the Greybeards, so he teaches you all 3 words of the Clear Skies shout. You can then clear the tempest and climb to the top to meet Paarthurnax. He will teach you the Fire Breath shout and you can discuss the matter of Dragonrend. And so you learn you are looking for an Elder Scroll. Actually one of the shortest and easiest quests of the game.
Elder Knowledge
This quest is quite long, probably to counterbalance with the previous one, which was very succinct. It can be parted in principally three phases.
Finding Septimus Signus
For a start, you must talk to Arngeir or Esbern. Regardless of who you ask, you will have to head for the college of Winterhold. Once upon the front door, you will have to get Faralda to open it for you (if not done yet, of course). There are several ways to do this, but accepting the trial of magic will get you. When inside, Urag gro-Shub, head of the arcanaeum, has to be located, so he can hand you some works about the Elder Scrolls. When you realize one of the books is unintelligible and tell Urag gro-Shub about it, he will send you to find Septimus Signus in the Sea of Ghosts.
Exploring the Alftand Animonculory and Cathedral
Septimus Signus will handle you the Attunement Sphere and the Blank Lexicon you will need to activate the Dwemer device containing the Elder Scroll. The device is located in Blackreach, which is under Alftand ground. So you head southwest of Winterhold, into the frozen corridors of the mountain caves. After facing a few bandits, you should reach a corridor that leads into the Animonculory. There you will face some Dwemer spheres and working spiders. Once you attain a circular catwalk that leads deeper into the ruins, you will encounter some Falmers; they can be very dangerous if you don't have sufficient level (for info: I was lev. 23 and got overwhelmed quite a few times). Sneaking around may save you from troublesome battles, so take them out discretely from a distance if possible. At some point, the bridge has collapsed, forcing you to jump down in order to keep pushing forward; just make sure you have explored sufficiently as returning above will not be possible, unless entering again from the Alftand.
Ultimately, after a good amount of traps and enemies, you will make it to the Dwemer Centurion chamber. Consider the duel with this robot as a boss fight, since its endurance is probably largely superior to your own. The best is to keep moving and try to lay damage from a distance, as its attacks are limited to average range. You will then enter a big room, which as the mechanism that will allow you to enter Blackreach. You still have a battle to attend, as two adventurers are already present. You can let one be killed by other, so you just fight one. Before you activate the entry to Blackreach, you can use the elevator up front to reach the surface and take a well earned break before the last part.
Crossing Blackreach and reaching the Oculory of the Tower of Mzark
Use the Attunement Sphere on the Dwemer mechanism at the end of the Alftand cathedral to gain entry to Blackreach. You will enter the vast underground plain: there you can find another elevator to the surface, Sinderion's lab and a Falmer citadel. Your destination is an elevator at the south west end; it is past a bridge to the left of the sewer entrance to the citadel. This will take you to the Tower of Mzark and you will find the massive Dwemer device containing the scroll in the Oculory. Walk up to the control panel and introduce the Blank Lexicon to activate the commands. Now press the button on the second cylinder to your left. You have to activate it until you lit the next button on the left and then activate the next button. Repeat until you all buttons are lit and you will gain access to the Elder's knowledge, at last!
NOTE: Remember to pick up the Lexicon for continuing 'Discerning the Transmundane' Daedric mission.