Endless Islands have no time limit, so you can explore the lands at your own pace. 

Where is the portal? 

The portal to a new island is somewhere on your current island. You can get a hint by tapping a portal icon in the Resource menu (bottom left).

 

Before you leave

Once you find the portal, you can travel to a new Endless Island at any time. If you decide to do so, be sure to collect all the bonuses and resources on your current island as it will close forever.