How does a metronome help in controlling breathing rate?
The paper in question used metronome to aid test subjects control their breathing rate. This seems like a good approach, much better, than asking "please, breath with 0.1Hz frequency".


  The subjects were asked to remain at rest in a supine position for 10 min, and then to control their respiratory rate with the help of a metronome at different breathing rates: 6 (near 0.10 Hz), 10 (near 0.16 Hz) and 16 (near 0.27 Hz) breaths/min.


Metronome is a device that produces any perceivable ticks (sound clicks or, maybe, light flashes can be used) with given and constant frequency. So patients were asked to synchronize their breathing with metronome clicks.

Only precaution in mentioned experiment is that high frequency of breathing can cause voluntary hyperventilation. Or if preset frequency is low and patient is trying to follow it, hypoventilation might occur. Fainting seems among the worst of consequences in both conditions (if person is relatively healthy).