First thing you will have to do is talk to the Valkyrie in Prontera, and ask her to warp you to the new world. She will give you the Ring of the Ancient Wise King, which you will need equipped for the majority of the quest.
I'm not sure if these steps are necessary, or if they are just implemented for Sakray testing, but I did this before talking to the Valkyrie so if you get stuck at the beginning, try these steps out as well:
Step 0. Getting to the New World
-Go to the Eden Group and speak to the Cat Hand Agent. Agree to work for him, pay him 50k zeny, and he will warp you to Morroc Field.

-Go directly right from where he warps you, and speak to the Cat. Jump on his back and he will take you to the Dimensional Rift.

-Go Directly north from where you appear, and speak to the Cat Hand Agent here. He will warp you to the New World.

Step 1: Invitation to El Dicastes
-Go outside the Command Center in the New World Base Camp, where you will see two NPCs talking. Speak to one of them (I talked to the guy on the left), and ask them what they are talking about. They will refer you to an NPC inside.

-Go inside and speak to the Blonde Haired NPC near the table. Accept his request to meet with the visitor.

-Go up the stairs to the right of you, where you will find 3 or so portals along the wall. Enter the portal with the guard standing in front of it. While in here (with Ring of the Ancient Wise King equipped!), speak to Hound, then the Sapha visitor, then Hound again.

-After you have been invited to El Dicastes, leave that room and enter the room directly above it. Speak to the NPC in here to pick of the beginnings of another quest, which I suspect may be the Scaraba Dungeon Access quest, though I havn't finished it yet so I'm not 100% sure.

Step 2: Passage through the Mines
-Head to the city of Manuk (from the midgard base camp, go east twice, south once). Once there, enter the large structure just south of the mines.

-Once inside, head to the back of the building and go up the stairs to the left (not through any portals). Continue following this path until you find Avalanche. Speak to him to get permission to enter the Mines.

-Leave this building, and go a little ways north of the building you were just in (marked by a red dot on the mini map). Speak to the Entrance Guard and he will teleport you into the mines.

-Travel through the mines to the City of El Dicastes. The exit to the mines is in the bottom right corner of the map, which can be reached by simply continuing to head east through the tunnel. In this map are Uni-horn Scaraba and Horn Scaraba, as well as their corresponding eggs.




Step 3: The City of El Dicastes
-Once you exit the mines, you will appear in the fields of El Dicastes. These fields are populated by centipedes, centipede larvae, Tatachos, and a new monster, Dolomedes.

-Head north from this field map to find the city of El Dicastes. Speak to the City Guards and they will teleport you inside.

-Once in El Dicastes, head directly north through the next portal.

-Continue heading north along the arched pathway, and enter the building at the north end. Finally, speak to the Adventurer's Clerk at the desk and register as an Adventurer. He will give you the Light of El Dicastes, which is an accessory that grants you the ability to teleport to El Dicastes at any time (with a 5 minute cooldown).

Congratulations! You can now return to El Dicastes at any time you choose, and have access to the first floor of the Scaraba Hole dungeon. I will post a guide for the Scaraba Hole floor 2 access quest once I've finished it, assuming of course no one else beats me to it!
Hope this is helpful!