With the activity tracker off your wrist, first hold the wristband towards one end of the screen, then gently pull the wristband out and push the device nugget down and out of the wristband. Note: the wristband should be pulled up and away from the nugget in relation to the screen of the device. This minimizes stretching of the wristband. 

To put the device nugget back in, take the wristband and slide the nugget in from the bottom, one side at a time.

A visual representation of this process can be seen here.