Tommy Stubbins, the narrator of the story, finds an squirrel injured by a hawk so the mussel man informs him to get help from Doctor Dolittle. Tommy goes to Mathew Mugg to find out where the doctor lives who tells him that the Doctor can speak the language of animals so they go to his house but find out he's gone away on a voyage and is guarded by the his dog Jip. Later the Doctor comes home to meet Tommy and takes care of his squirrel then explains when Tommy see's a strange fish creature in his house that it's a Wiff-Waff and is trying to learn shellfish language but eventually he quits it as it is too hard to study. Unexpectedly Polynesia turns up in Puddleby from Africa who imforms the Doctor that Bumpo is studying in Bullford then Tommy gets the Doctor, with the help of Poynesia, to teach him the animal languages. After Polynesia teaches Tommy the language of animals, so he can understand Jip and Dub-Dub, Chee-Chee comes from Africa disguised as a lady and tells about his voyage to Puddleby. The Doctor then gets a vessel called The Curlew and is thinking of taking Tommy, Polynesia, and Luke the Hermit. They find out from the hermit's dog, Bob, that he was sent to prison for murder but Bob is a witness so when the court is in process the Doctor proves to the judge that he can talk to animals, when this is settled he translates Bob's story to english. When the story is finished the judges conclude that the hermit is innocent.
Later the Purple Bird of Paradise informs the Doctor that Long Arrow, son of Golden Arrow, who is a friend of the Doctor, is missing so after they play the game Blind Travel, which would determine where in the world they would voyage, they decide to take a trip to Spider Monkey Island to find Long Arrow. The Doctor, Tommy, Bumpo, Polynesia and Mathew start the voyage across the sea but on the way they discover some stowaways and drop them off at the coast off Puddleby. Their first stop is Spain where a bullfight is in process so the Doctor makes a deal with the bullfighters that if he can beat them in a fight they would agree to stop bullfighting ever again. The Doctor talks to the bulls and they agreed to stick to the plan to make everyone think that he outwitted them. When the fight is over and the doctor wins against the other bullfighters the people protest because of bullfighting being banned. When the doctor and his crew set off again the Doctor shows Tommy he has caught a fidgit that talks english so he consults it and finds out that to go underwater deeper to observe the ocean is to find the Pink Sea Snail.
Afterwards there is a storm which wrecks the ship leaving Tommy alone without anyone in sight then the Purple Bird of Paradise tells him that his friends are on Spider Monkey Island so with the help of the porpoises Tommy reaches the island and the crew. The doctor finds out from catching a Jabizri, a rare beetle, that Long Arrow is stuck inside Hawk's Head Mountain so they try to find an opening but fail so they use the Jabizri to locate it. When the find a slab in the mountain they dig under it until it collapses and Long Arrow is free. The Doctor finds out from the people of the island that the island is going southward and is going to perish so the doctor gets some whales to push the island back to South America. After this the Doctor is told by the Popsipetels, the people of the island, that they will be attacked soon by their rivals the Bag-jagderags so the Doctor uses the birds of the island as well as the Popsipetels to battle them. The Doctor and his army win but the people then decide after so much he did for them that they would crown him king of their island. So for many months the doctor rules the island and makes good changes for the Popsipetels and everything as he stays king. One day though Polynesia spots the Pink Sea Snail so she and Tommy tell the Doctor about it which makes him interested in speaking shellfish language again. He talks to the Pink Sea Snail and learns that it is because of the island colliding with South America that it ends up on the shores of Spider Monkey Island so the Doctor asks the snail to take him in his shell with his crew back to England. The Doctor abandons Spider Monkey Island and sets off with Polynesia, Tommy, Mathew, Chee-Chee and Jip and makes his journey through the ocean in the shell of the Pink Sea Snail. When they come back to England the Doctor and his crew go back to Puddleby in the doctor's house and Dub-Dub says they are just in time for tea.

Question: How did they decide where to travel after talking to the purple bird of paradise?
Answer: By playing the game Blind Travel
Alternative answer: They played blind travel