Sleep tracking is done automatically by the Fitbit One device. When your body is in resting place and you're sleeping without moving, the device automatically records the data automatically.
By default, unless there is a heart-rate monitor, the device will track time spent awake, restless, and asleep. This data can be synchronized afterward.
In the morning, the device should synchronize the data with the application on your PC and display reports and statistics.
For additional information, I recommend checking the Help section on the developer's website to see exactly how sleep is tracked an recorded.