A black screen or no image on the Fire Stick is usually caused by the incorrect HDMI input being selected on the TV. If your TV displays a no signal error message, try selecting another HDMI source via the TV remote's input or source buttons.
Another common cause is that the device doesn't have enough power to function properly or turn on as it should. Ideally, the Fire Stick should be attached directly to the wall. Power adapters and surge protectors are known to affect the stability of media devices such as streaming sticks.