Serana knows a secret way into the castle's courtyard. There is an inlet on the north side of the island that was once used for bringing in supplies. An escape tunnel exits there. That is how you will be entering. The secret entry is around the side of the castle.

Fast travel to castle Volkihar. Cross the bridge towards the gate, but instead of making it all the way to the main gate, break left and jump over the ridge. Swim (or climb) around the side of the island to reach the northern part. Defeat the skeletons there and enter the Volkihar Undercroft. Open another door to get to a section with a bridge. Don't cross the bridge yet but rather go north. Then turn right and climb some steps, find a lever in a small room and activate it. Jump down and go west on a wooden plank, then south. Go through some tunnels and find some more stairs, climb them to get to a cave filled with spider webs. Break through the webs, defeat the spider behind and activate the lever that is near the window.

Go back down to where the narrow wooden plank was, and this time turn west and climb up the long stairs. The stairs turn south, then lead to a door. Open the door and enter the Volkihar Courtyard. There is a big moondial in the center of the courtyard which is missing some crests.

Volkihar Castle Moon Dial Puzzle Solution

All crests are located in the area around the moondial. See directions and images below on how to find each crest:

Crescent Moon Crest
Near wooden table to the NE up some stairs

Crescent Moon Crest Dawnguard

Half Moon Crest
Northern part of the courtyard, in a small pond

Half Moon Crest Dawnguard

Full Moon Crest
Search the wall to the east, the crest is laying against the wall

Full Moon Crest Dawnguard

Place the crests in their corresponding locations on the moondial (if its the incorrect location it wont accept it, just try the next location). The moon dial spins and a secret entrance is revealed. Go down the stairs into the Volkihar Ruins.