Goblin Civil War
Go talk to General Bentnoze or General Wartface in Goblin Village. They will say that the goblins are on the brink of civil war over which color armor is best, they will ask you to bring them a sample of orange armor to try.
Gathering the Items
Ask the generals where to get Goblin mail and how to get Orange goblin mail and a general will tell you that you can find Goblin mail in crates and that to get Orange goblin mail you dye normal Goblin mail orange. They will also mention that Grubfoot stole some Yellow dye from a witch in Draynor, and that perhaps that would be a good place to find Orange dye. Then you will need to take the armor from the crates: behind the generals' hut, next to the western hut and up a ladder near the entrance. Then it's time to make the dyes (Note: You can skip to section 7 if you already have Orange dye and Blue dye. It is possible to buy them from the Grand Exchange. Alternatively you can buy all the ingredients and skip to section 6.).
Walk (or teleport) to Varrock, go out the eastern entrance and walk south to the south-east mine. Just a bit to the north-west of the mine (between the mine and the city wall) there are two types of bushes. Take three Redberries from the red bushes. (Note: Do not eat the Cadava berries from the pink bushes. They are poisonous.)
Walk (or teleport) to Lumbridge and from Lumbridge castle walk north and then west along the path to Farmer Fred's farm next to the sheep pen, around the back you will see an Onion patch, pick two onions.
Follow the path (or teleport) to Falador and go to Falador Park. Talk to Wyson, the head gardener, near or in the building at the east of the park. Ask him if you can buy some Woad leaves. Wyson will ask how much you are willing to pay, say 20 coins and for your generosity he will give you two.
Making the Dyes
Walk back south out of Falador (or use cabbage port to the cabbage patch) and go to Draynor Village. Talk to Aggie the witch and ask her is she can make you anything. She will say she can make dyes. Ask her to make Blue dye, Red dye, and Yellow dye (each dye will cost you 5 coins) and use the Red dye with the Yellow dye to make Orange dye.
The Generals' Verdict
Go back to Goblin village and dye one Goblin mail orange, one blue, and leave the last one brown. Speak to the generals and give them the Orange goblin mail. They will have Grubfoot try it on, and say they do not like it.
Then they will ask for Blue goblin mail, give them the Blue goblin mail and again they will have Grubfoot try it on, and again it they will say they don't like it.
They will then want brown. Give them the plain brown Goblin mail. They will have Grubfoot try it on and this time they decide that the original color is best after all!
Congratulations! Quest Complete!