Shipyard

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This article concerns content exclusive to Warlords of Draenor.

The Garrison Shipyard (called "Frostwall Shipyard" for Horde and "Lunarfall Shipyard" for Alliance) is a new building and extensive new feature introduced with Patch 6.2. A path has opened up from your garrison to the coast (you may remember the shipwreck you encountered when establishing your garrison) that leads to the new shipyard.

Level 1: Build ships and run naval missions from the coast near your garrison.
Level 2: Build ships and run naval missions from the coast near your garrison.
Level 3: Build ships and run naval missions from the coast near your garrison.

Source

Your character needs to be level 100 and have a level 3 garrison.

There are basically two short quest chains that need to be completed to start running your shipyard. The first involves visiting the Iron Docks to find a an orc shipbuilder for your shipyard and the second involves establishing your base in Tanaan Jungle.

Constructing the Shipyard

This quest chain begins with talking to either Varian Wrynn or Vol'jin inside your Town Hall. The chain is called "All Hands On Deck" in the achievement In Pursuit of Gul'dan.

Alliance

[100] Garrison Campaign: War Council - Talk to Varian Wrynn who will direct you to fly to the Iron Docks.
[100] We Need a Shipwright - Fly to Iron Docks via your garrison flight master.
[100] Derailment - Find Explosives and Detonator. You can do the optional bonus objective while there for 200 [Garrison Resources] and some gold.
[100] The Train Gang - Plant three explosives on nearby train and use the detonator to free shipbuilder Solog Roark.
[100] Hook, Line, and... Sink Him! - Find a grappling hook and shoot up to the balcony to kill Admiral Knar and obtain Roark's Shipyard Blueprints. You're basically done with the Iron Docks part.
[100] Nothing Remains - Turn in at to your Garrison. It's good idea to have [Garrison Hearthstone] ready.
[100] All Hands on Deck - King Varian gives you a quest which unlocks the level 1 Shipyard. The construction requires 150 [Garrison Resources] and 150. Take the path throughout the gate near the Pet Menagerie to go to Roark at Eventide Landing; an in-game cinematic will start after turn-in.

Horde

[100] Garrison Campaign: War Council - Talk to Vol'jin who will direct you to fly to the Iron Docks.
[100] We Need a Shipwright - Fly to Iron Docks via your garrison flight master.
[100] Derailment - Find Explosives and Detonator. You can do the optional bonus objective while there for 200 [Garrison Resources] and some gold.
[100] The Train Gang - Plant three explosives on nearby train and use the detonator to free shipbuilder Solog Roark.
[100] Hook, Line, and... Sink Him! - Find a grappling hook and shoot up to the balcony to kill Admiral Knar and obtain Roark's Shipyard Blueprints. You're basically done with the Iron Docks part.
[100] Nothing Remains - Turn in at to your Garrison. It's good idea to have [Garrison Hearthstone] ready.
[100] All Hands on Deck - Vol'jin gives you a quest which unlocks the level 1 Shipyard. The construction requires 150 [Garrison Resources] and 150. Take the path throughout the gate near the Pet Menagerie to go to Roark at Eventide Landing; an in-game cinematic will start after turn-in.

Setting up a base in Tanaan Jungle

The chain is called "The Invasion of Tanaan" in the achievement In Pursuit of Gul'dan.

Alliance

[100] - Go see <Shipyard Foreman>, Merreck Vonder, who will direct you to meet Solog Roark at the beach to east. Upon completion you are rewarded with 300 [Oil].
[100] - Solog gives you [Ship Blueprint: Transport], so right-click it in your bag to learn how to build a Transport.
[100] Strange Tools - Go see night elf <Shipwright>, Yanas Seastrike down the beach to the right of the docks.
[100] Ship Shape - Construct your first Transport work order with Yanas. Building the ship should take only 1 minute and then you can right-click with the gear pointer to finish the ship.
[100] The Invasion of Tanaan - Go to the other side of your Shipyard where the docks start and talk to Yrel to take your Transport to Tanaan Jungle.
[100] Obstacle Course - Once you land, turn in to Draka and accept this quest. Find two items guarded in Iron Horde buildings by an orc warrior Rulkrik the Pillager and an orc warlock Magril the Seer: a scroll on the left side of the road and a book from farther down on the right side of the road. Turn in the quest to Exarch Naielle who waits stealthed on the road to north.
[100] In, Through, and Beyond! - Pass through the gate to west, avoid the cannon fire and mobs (if you run past them, only a couple will remain to kill as you near the cannon), and destroy the cannon on the hill by right-clicking the pile of spiky bombs. You may have to kill a warrior and caster mob to get to the bombs. Afterwards meet Naielle near the south wall.
[100] The Assault Base - Follow Naielle to the nearby clearing to establish your base of operations in Tanaan Jungle, Lion's Watch, by right-clicking the Alliance banner.

Horde

[100] Let's Get To Work - Go see <Shipyard Foreman>, Rolosh Wavechaser, who will direct you to meet Solog Roark at the beach to east. Upon completion you are rewarded with 300 [Oil].
[100] Shipbuilding - Solog gives you [Ship Blueprint: Transport], so right-click it in your bag to learn how to build a Transport.
[100] Ship Shape - Construct your first Transport work order with Solog. Building the ship should take only 1 minute and then you can right-click with the gear pointer to finish the ship.
[100] The Invasion of Tanaan - Go to the other side of your Shipyard where the docks start and talk to Draka to take your Transport to Tanaan Jungle.
[100] Obstacle Course - Once you land, turn in to Draka and accept this quest. Find two items guarded in Iron Horde buildings by an orc warrior Rulkrik the Pillager and an orc warlock Magril the Seer: a scroll on the left side of the road and a book from farther down on the right side of the road. Turn in the quest to Shadow Hunter Mutumba who waits in stealth on the road to north.
[100] In, Through, and Beyond! - Pass through the gate to west, avoid the cannon fire and mobs (if you run past them, only a couple will remain to kill as you near the cannon), and destroy the cannon on the hill by right-clicking the pile of spiky bombs. You may have to kill a warrior and caster mob to get to the bombs. Afterwards meet Mutumba next to a tree directly west from the cannon.
[100] The Assault Base - Follow Mutumba to the nearby clearing to establish your base of operations in Tanaan Jungle, Vol'mar, by right-clicking the Horde banner.

Shipyard intro

Your Shipyard is ready to go. You will need to do some simple introductory quests to build some ships and complete a few missions (the first mission will always fail, even at 90+% chance, and destroy your first destroyer, but don't fret). The guaranteed fail mission is also there to teach you that unlike follower missions, naval missions run the risk of losing a Garrison ship.

You will also see the first blockade naval mission which needs to be completed to open up certain areas and their missions.