If your product is connected to the power supply, check if the lights on the controller are on.
A continuous blue LED on shows your product is connected to the local Wi-Fi network. Check to see if your smartphone is connected to the same Wi-Fi network.
If the blue LED flashes it means it is trying to connect to the local Wi-Fi network but something is stopping it. Try to move the Twinkly nearer to the router to solve the problem.