After you complete the Ancient Cistern dungeon, your next task is to visit the Isle of Songs. From there, you should go to Lanayru Desert.
Learn Nayru's Wisdom
Fly to the Isle of Songs in the thunderhead. Crawl into the tower and use a skyward strike on the crest to learn a new song called Nayru's Wisdom. Fi will tell you that the next trial is in Lanayru Desert.
Nayru's Silent Realm
When you dive down into Lanayru Desert, choose the Northern Desert bird statue. The gate to the silent realm is near the electricity dial in the north part of this area. Go to the butterflies and sparkles and strum your harp, then play along with the pulsing circle of light to reveal the portal. Follow the on screen instructions to thrust your sword into it.
Once you are in Nayru's Silent Realm, you will notice that the Tears of Nayru are all somewhat far away from you. Worse, there is a guardian between you and the nearest tear, so you will have to run forward to the steps leading up to the Mining Facility to get Tear #1. The guardians are actually somewhat easy to outrun, as long as you don't let your stamina get too low. Hold the A button to put some distance between you and the chasing guardian(s), then stop running to allow your stamina to refill, then start running again when the guardian gets close.
Now hold the A button to run onto the ledge that has the generator on it, where you turned the three dials in the past. You should be able to run onto this ledge from the stairs leading up to the mining facility. Tear #2 is in front of the generator.
Run toward the gate to the silent realm, then go get Tear #3 from the northeast corner of the map.
Run southwest along the submerged wall. Go to the left when there is a ramp to your right. This will lead you to a ramp up to where Tear #4 is on a platform on the east side of this area.
Run west along this wall and go down the slope, then go up the slope to the right. Be careful of the poes up here. The poes on this wall go back and forth. Follow behind the first one, making sure not to let the poe's light shine on you, and then hide out on the spot on the right. Watch the movements of the poe on the right, then emerge from your hiding place and run to the ledge with the guardian on it when both poes are safely out of your way. Then collect Tear #5 when the poe here is not shining its light on it.
Make sure you are not out of stamina and jump off the ledge to the left, then run up onto the ledge at the base of the tower. Go to the left and get Tear #6 from the boxes leading up to the upper level. Stay at the level at the top of the boxes and go around the tower to get Tear #7 and Tear #8 from the surrounding boxes as well.
Still on the tower, run to the southwest of the tower and climb up the vines from the second level. Then turn left from the top of the vines and go clockwise around the tower to find vines on the east wall of the tower. Climb to the top of the tower to find Tear #9.
Now go southeast from the tower, in the direction of the building where you activated the fire dial earlier in the game. You will see a tear hovering in the air with a mine cart nearby and some waking water rising and falling around the mine cart. Pull the mine cart toward the tear when the water goes down. Don't push the cart. You're too likely to get caught in the waking water if you push it. While pulling it, you should let go and run away when the water rises, then go back and pull the cart the rest of the way. Run onto the cart and get Tear #10.
To the south, there is a mine cart up against the wall. Run up it to get Tear #11.
Now hop down and turn right. There is a mine cart that you can push against a cage to run up and reach Tear #12.
Turn left and hop down, then run up the slope to get Tear #13 from the ledge just south of where you got the tear from the top of the cage.
Look to the south and you will see a tear to the right and a tear to the left. Go to the right of the long wall and run to the tree. Hold down the A button and shake the nunchuk to do a roll attack into the tree and knock down Tear #14.
Go east and carefully hop down the tall wall, avoiding the light of the poes. Turn right and carefully make your way around the field of poes, avoiding their light and trying not to get close to them. You will find Tear #15 at the south end of the map.
Now that you have all 15 Tears of Nayru, the timer will no longer count down. You are free to explore this area at your leisure and look for Dusk Relics, but be careful to stay away from poes and waking water.
Receive the Clawshots
When you return to the exit of Nayru's Silent Realm, you will receive the clawshots. You can use them to pull yourself to targets and vines. In addition, if you are hanging from a target or some vines, you can use use the other clawshot by pressing B and choosing your next target.
Find Goddess Cubes and Treasure
Back in Lanayru Desert, go around and look for wall targets. You can now access Goddess Cubes and a blue chest containing a Dusk Relic.
The dusk relic is in a blue chest close to where you entered Nayru's Silent Realm. Use the clawshot to hit the target and climb up onto this ledge.
One goddess cube can be reached by bombing the wall east of where you turned on the electricity dial. Go to the end of the cave and use the clawshots to make your way along the path. Then you will reach a ledge with a goddess cube on it.
The other goddess cube is on a ledge in the southwest that you couldn't reach before. Stand on the tower and look around if you have trouble finding it. You can reach it by hitting a clawshot target.
Reach the New Area
You can see on your map that there is an area to the west that you couldn't access before. The easiest way to get there is to go back to the sky, then dive down at the Western Bird Statue. Use the clawshot to get up onto the ledge, then push the mine cart down to give yourself a shortcut. On the ledge, go toward the falling sand and hop along the rocks near the cave opening up above. Use the clawshot to get up there and go inside.
In here, you will meet Golo, who is digging at the wall. Talk to him to receive a key to the door in here. If you sit in the chair near Golo, he will ask you to invest 10 rupees in his excavation.
Use the clawshots to reach the locked door and go through.