Hail to the Troll!
Make your way to Miscellania via either Fairy Ring (CIP) or taking the boat from Rellekka. Enter the kingdom and take the stairs up to the second floor, where Vargas will be waiting. Enter the throne room and a guard will try to stop you, but when you say you're from the heroes guild he will let you in.
Talk to Vargas to begin the quest. He will tell you about himself and why he's a troll, and then claim he's looking for a Regent. Offer to take that role and Vargas will tell you that you must show your worth by negotiating peace with Etceteria and marrying his son or daughter, and that you must also have the public's support if you wish to become Regent.
Give Peace a Chance
Note: This part of the quest requires a lot of running around!
Talk to Advisor Ghrim (located to King Vargas' right) and ask him how to make peace with Etceteria, where he tells you it would be a good idea to talk to their Queen, Sigrid. Leave Miscellania and follow the path over the bridge and into Etceteria's kingdom.
Talk to Queen Sigrid and tell her that you have been sent by King Vargas to negotiate a treaty. She says she will agree to a peace treaty if King Vargas recognises Etceteria as a sovereign nation. Go back to Vargas and tell him what Sigrid had said. He says he will recognise Etceteria if Sigrid changes her delightfully insulting anthem.
A New Anthem
Go back to Sigrid and talk to her. She will sing her anthem and then agrees that she will change the anthem if you come up with it. Go back to Miscellania and talk to Prince Brand to get an Awful Anthem. Talk to Advisor Ghrim and give him the poem which he will then change into a Good Anthem.
Head over to Queen Sigrid again and she will read out the new Anthem. She says she is pleased with it and will give you a Treaty, which only needs to be signed by King Vargas.
My Hands are too Big!
Take the treaty to King Vargas and tell him he needs to sign it. He says he can't because his hands are too big for a normal-sized pen and he'll need a larger one. Head to the coal mines on the northern shore of Miscellania and head into the eastern building with the anvil in it.
Talk to Derrik and tell him about your strange request for a giant pen. He says he can make a Giant Nib if you give him an Iron Bar. Give him one and he will give you the Nib, which you then can use on the Logs in your inventory to make a Giant Pen. Give the pen to Vargas and he will sign the treaty.
Talk to Advisor Ghrim and ask him how to get married to either the Prince or Princess, and he will tell you blandly that talking to them would be a good idea.
If your character is female, enter the room south of the Throne Room and talk to Prince Brand. You will tell him of your goal to become Regent of the Kingdom, and he will interrupt and ask why he would be interested in you, but will give you a chance to impress him. Continue talking to him and when he asks you a question answer with the most flattering answer.
He will eventually ask if you would like to hear his poem. Tell him that you would love to and he will recite it for you. Choose "Be still, my heart" and use the Clap or Cheer emotes.
Talk to him more, continuing to flatter him with answers and then give him some flowers. He will ask if they're for him, which you answer "Yes". Continue to talk to him and eventually give him the cake, saying it's for him. Talk to him more until he calls you "darling". Then do the Blow Kiss emote and give him the Ring. If he says he can't accept it talk to him more and keep trying until he says yes, and that you should tell King Vargas that you are getting married.
If your character is male, enter the room north of the Throne Room and talk to Princess Astrid. You will tell him you wish to become regent. She will say she has many suitors but give you a chance to impress her. Talk to her a few times and agree with whatever she says. Give her the Flowers and then use any Dance emote (Dance, Headbang, Twirl, Jig, Snowman Dance, or Zombie Dance).
Talk to her a few more times and answer with the most agreeable answers. Once she has nothing left for you to agree with, give her a bow. Talk to her more and when she calls you "dear" and then use the Blow Kiss emote.
Talk to her more and continue to agree with her until you have nothing left to agree on. Use the Blow Kiss emote on her again and give her the ring. Finally she will agree to marry you and say that you should tell her father.
A Helping Hand
After you get engaged, talk to King Vargas and tell him his son or daughter has agreed to marry you. He tells you the population is not very supportive of you becoming their Regent. Talk to Advisor Ghrim and ask him how you can get the public's support. He says that helping them with their daily tasks and tell you currently only 25% of them support you. Your objective is 75%.
A popular way to gain support is raking weeds from the herb and flax patches just outside the Walls. It requires 10 Farming and 30 Herblore. It is the fastest method for gaining support at a rate of 1% per 1.285 Weeds.
Another way to gain support is to mine Coal in the Mines on the north shore of Miscellania. It's the second quickest way to gain support at a rate of 1% per 1.285 Coal. The is also a possibility to find a gem which you can give to Miner Magnus which gives you 5% more support.
You can chop Maple Tree's in the grove outside the kingdom. It's a very slow method of earning support as they are reasonably hard to cut down and you gain support at a rate of 1% per 2 logs.
You can fish Tuna and Swordfish with a harpoon or Lobsters with a Lobster Pot off the docks of Miscellania. You gain support at a rate of 1% per 1.285 fish, regardless of what fish it is. It's recommended you have your game messages filtered so you're chat screen isn't spammed with fishing messages.
The New Regent
After you've gained 75% of the public's support, talk to King Vargas. If you gain 100% support, a villager will stop you and say you've done enough work. King Vargas will go through a short ceremony and name you Regent of Miscellania.