In Silvermoon City you need to go the Sunfury Spire, pictured in the map below (it is near at the top of the map, near the middle). The Inner Sanctum has a teleport which will take you to the Undercity.
Sunfury Spire is at the top in the middle
Directly outside the Undercity are zeppelin towers, pictured below. The tower on the left in the picture will take you to Orgrimmar. There are Goblins at the front of each landing pad who will tell you which city this zeppelin is for, and where it is on its trip (intended to give you an idea of how long you'll be waiting). For example: The zeppelin for Orgrimmar has just left Orgrimmar.
If you've got a Blood Elf friend and they want you to come play with them, you'll likely be traveling from Orgrimmar to Silvermoon. Silvermoon is located on a different continent, so you'll have to take the Zeppelin to get across the sea to Undercity. From Undercity you can use a teleporter to go directly to Silvermoon. You'll need the Burning Crusade installed in order to be able to access Silvermoon.
Find the Zeppelin Master in Orgrimmar. You can find the Zeppelin tower to the east of the Orgrimmar main gate, between The Valley of Strength and The Drag. Look for the Zeppelin that will take you to Tirisfal Glades (Undercity), which can be found on the south side of the tower.
Board the Zeppelin. The Zeppelin arrives every few minutes. Hop on board when it shows up, and then wait to arrive at Tirisfal Glades.
Get off the Zeppelin at Tirisfal Glades. If you look to the south from the Zeppelin tower, you'll see the gates to Undercity.
Travel south to reach Undercity. The gates to Undercity are directly south of the Zeppelin tower, just a few paces away. Head through the gates to enter Undercity.
Enter the Ruins of Lordaeron. This is the first area you enter when you pass through the Undercity gates. You'll see a gazebo in the center of the courtyard. Head south towards the gazebo structure and then look to your right.
Walk up the stairs to the west. The Ruins of Lordaeron is a large courtyard area at the entrance of Undercity. Take an immediate right from the central gazebo in the Ruins and walk up the staircase.
Enter the chamber at the top of the stairs. Enter the chamber at the top of the staircase. You'll see the Orb of Translocation at the center of the room.
Use the Orb to teleport to Silvermoon. You will end up in the Inner Sanctum of the Sunfury Spire in Silvermoon City. If you need to get back to Orgrimmar, you can follow the steps in reverse.
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