Visit Levias in the Thunderhead to learn the Song of the Hero, then go to Skyloft and play the song near the butterflies near the Light Tower to open the Goddess's Silent Realm.
Learn the Song of the Hero
After you have learned the Thunder Dragon's Song, the Water Dragon's Song, and the Fire Dragon's Song, you can learn the Song of the Hero if you haven't already. Go back to Levias in the Thunderhead and land on Levias's head like you did when you fought Bilocyte. Don't use the Sailcloth, or Levias might go too far ahead for you to land. Levias will teach you the song and Fi will make it possible for you to dowse to find the place of the trial.
Find the Trial Gate
Land on Skyloft and you can dowse for the trial gate to reach the Goddess's Silent Realm. The gate is near the Light Tower.
Collecting the Goddess's Tears
Collect Tear #1 straight ahead, near a Guardian.
Turn around and climb up the Light Tower, avoiding the Watcher that circles around the upper level. At the top, find Tear #2.
Look toward the Bazaar to see Tear #3 in front of a Guardian. To get it, just fall off of the Light Tower since you can't lose hearts here, but be careful not to fall off of the edge of Skyloft. Then get the tear.
There is a Watcher going back and forth over the wooden pier nearby. Carefully avoid it to get Tear #4. After you get the tear, you may need to hide behind the Guardian at the end of the pier to wait for the Watcher to go away.
Go to the east side of the Bazaar and get Tear #5 under the tree.
Jump down to the lower area and avoid the Watcher to cross the stone bridge to the residential area. There is Waking Water below the bridge, so be careful not to fall in. Get Tear #6 from the center of the bridge. Then go toward the east side of the bridge and run north off of the stairs to avoid the Watcher.
Go south to the graveyard, being careful to avoid the Watcher that floats there. Get Tear #7 from the far end of the graveyard.
Carefully avoid the Watcher again to get out of the graveyard. If you go north and look to the right, you see a growing and shrinking pool of Waking Water under the bridge between houses. When it recedes, go past it and get Tear #8.
Wait for the Waking Water to recede again and go west past it. Go north to where four Watchers are floating around a tear. Wait for there to be a gap between their lights and run to Tear #9 in the middle. Wait for another gap to appear between their lights to run out of their area.
Go west across the stone bridge toward the Bazaar, avoiding the Watcher. Head north to the stepping stones in the water. Get Tear #10 just before the stepping stones.
Go across the stepping stones to get Tear #11 on the other side.
Go back across the stepping stones, then look west to see the narrow wooden bridge beyond the tree. Go west along the wooden bridge and carefully avoid the Watcher to reach Tear #12 on a narrow piece of wood.
While avoiding the Watcher, go west, then go south when you can, and go up the stairs on the left. Go northeast from there and go up the stairs from the north end of the Bazaar to get Tear #13 at the top.
Go between the fences in front of the Knight Academy entrance and carefully pull the wooden crate back, letting go to run away from the Watcher's light when it comes near. The tear will cast a shadow of light on top of the crate when the crate is under it. Climb up onto the crate (walk toward it until you climb up) and get Tear #14.
Finally, go slightly east to get out from between the two fences, then go south so that you can go west toward the Knight Academy without being between the two fences. Run up the wall of the Knight Academy to grab the wooden ledge, then go to the left until you can drop down onto the awning. Jump to the next awning, then climb up the vines to reach the roof. Go around the edge to keep your distance from the Watcher, and get Tear #15.
Carefully make your way back to the entrance of the Silent Realm in the southwest, avoiding Watchers and Waking Water.
When you step into the protective circle to leave the Goddess's Silent Realm, you will receive the Stone of Trials.
Opening Sky Keep
Go to the stone statue of a bird near the stepping stones on the north side of the eastern lake. Examine the statue to put the Stone of Trials in place of the missing eye. A structure under the Goddess Statue will appear, and some floating Clawshot targets will appear. At the last Clawshot target, you can let go to drop onto the ledge that leads into Sky Keep.