Walkthrough
Osman: He can be found outside the palace. Talk with him, and ask him what you have to do.Leela: She can be found east of Draynor. Talk with her.
Wig and Rope: Get some wool (use shears on sheeps, wich can be bough for 1gp in general store), and use it on a spinning weel. You will need 7 balls. Talk with Ned in Draynor Village, and he'll make it for you.
Skin Color and Dye: Get ashes, flour, water and rederries and 2 onions. Go to Aggie in Draynor Village, and ask her to make you a skin past. Then ask her to make you a yellow dye, it will cost you 5gp. Then you have to use the dye on the wig.
Pink Skirt: You can buy a pink skirt in the clothes store in Varrock, it normally costs 2gp.
Leela: Talk with her again, and ask her about a key.
Key: Get some soft clay and bronze bar. Now, go talk with Lady Keli in the jail. Tell her that she's famous in RuneScape, then ask her for her latest plan, then ask her if she's sure they will not try to get him out, ask her to see the key, and then ask her if you could touch it. Now, you will have a print of the key. Go to Osman.
Osman: He will take the key print and the bronze bar. Go back to Leela to get the key.
The Guard (Joe): Talk with him, and tell him to chill out, you won't make any trouble. Then ask him about what he do with the wages, and he tells you that he like to drink. Now, go get some beer. You can find it in north part of Barbarian Village. Pick up three of them.
The Rescue: Talk with Joe again, and ask him if he would fancy some beer. Then use the rope on Lady Keli. Now, use the key on the cell door, and talk with the prince. He will tell you that you will get a reward from Hassan. Go back to Hassan to claim your reward.