You can leave through the Home function of the site to reach other new islands. But the normal way is to use the walkie talkie to reach the blimp at the oil rig.
If you see that you are not getting the walkie talkie when in the helicopter, reset the island using the small map at upper right (press the blue button "Restart Island").
you use the walkie talkie for your helicopter
You use your walkie talkie in your bag to get the helicopter to come.
First, you get out of the prison building. Then, you go to your items and use the walkie talkie to call up the helicopter dude.
To leave the island once you get on the helicopter, you have to go through the security screening on the island (then the storm stops). Return to the guards area, exit the prison, and call the helicopter on your walkie talkie.
The helicopter arrives on the roof of the drilling platform when called by the rig boss, or by the walkie talkie. At the Erewhon Prison (anagram of "nowhere"), it arrives just outside the hidden entrance.
To leave the island, you have to go back to the oil rig. Leave the lab, exit the prison, and call the helicopter on your walkie-talkie. He will take you back to the oil rig. Once you are heading to the island, you have to complete the prison security before you can call the helicopter.
The helicopter arrives on the roof of the drilling platform when called by the rig boss, or by the walkie talkie. At the Erewhon Prison (anagram of "nowhere"), it arrives just outside the hidden entrance when you call it.
Since "Main Street" is the drilling platform, all you have to do is call the helicopter on your walkie-talkie to leave the prison. *For a shortcut, get the Haunted House card from the store. Entering then leaving that game puts you on the Island Map.
Once you have done a parachute jump from the helicopter, you have the Walkie Talkie that lets you call the helicopter to take you back and forth to the oil rig and prison. However, once you beat the island, there is literally nothing to do at the prison.
To leave whether completed or not, go outside, use the walkie talkie, and fly in the helicopter back to where you can catch the blimp (the oil platform). (You cannot leave until you have passed through security in the prison. The storm stops while you are in the guard room.)
The Walkie-talkie
You will travel to a secret maximum security prison to engage in a dream experiment on 4 captured super villains. You will enter their dreams to collect totems that represent their evil. You arrive at an oil rig from which Dr. Jupiter has been recruiting "assistants" for his experiments. The rig supervisor's office is at the top of the rig, and you will get a helicopter ride to the mysterious island where the prison is located. (To leave Super Villain Island, you must pass through security at the prison, and the storm will pass, so that you can call the helicopter on your walkie-talkie.)