In order to gain access to the Inner Sanctum, where Vyrthur and Auriel's Bow are located, you need to fill your initiate's ewer with water from the basin of the following five wayshrines:

Wayshrine of Illumination
Wayshrine of Sight
Wayshrine of Learning
Wayshrine of Resolution
Wayshrine of Radiance

You can visit them in any order, however this guide suggests a logical path which will let you find all the wayshrines quickly.

Touching the Sky Wayshrine Locations

1) Wayshrine of Illumination
This one is at the end of Darkfall Passage. You get to Darkfall Passage by taking the portal in the shrine behind Gelebor in Darkfall Cave. This shrine is guarded by Prelate Sidanyis. If you are currently in Forgotten Vale then you most likely filled the ewer already, since the portal to Forgotten Vale is after that wayshrine.

2) Wayshrine of Sight
From where you entered Forgotten Vale (after taking portal from Wayshrine of Illumination in Darkfall Passage), follow the road north and west and go down into the valley. The Wayshrine of Sight should be nearby. It is guarded by Prelate Athring.

3) Wayshrine of Learning
From the Wayshrine of Sight, go southwest up a path in the hills. Reach a river and swim a little downstream, then exit the river and climb southeast. The Shrine of Learning is guarded by Prelate Celegriath.

4) Wayshrine of Resolution
From Wayshrine of Learning, go back down into the river and follow it northwest. Climb some stairs onto the mountain,  follow the path and cross the bridge west. You will arrive at the Wayshrine of Resolution, which is guarded by Prelate Nirilor.

5) Wayshrine of Radiance
This is the last wayshrine. From the Wayshrine of Resolution, cross the bridge back to the other side, then go downhill onto the river and fight it upstream. Keep heading south along the river until you reach the entrance to the Glacial Crevice. Enter the Crevice and work your way to the other side of it, and exit from the south side back into the Forgotten Vale. Go southeast in the ravine past the Falmer camp. Enter another tunnel to the south. Traverse the tunnel south and west, and exit it on the west. Follow the road a little and arrive at the Wayshrine of Radiance, guarded by Prelate Edhelbor