I'm reading an English translation of Ramana Maharshi's Upadesa Sara with commentary and verses 11-14 talk about controlling the breath (pranayama). A few relevant points made in those verses:
* Controlling your breath can help quieten the mind.
* There are such things as harmful breathing patterns so it's important to seek the guidance of experts to avoid them.
* The simplest breathing exercise that's easy to do right without an instructor is to observe the breath as it is.
I've made a conscious effort to observe the breath randomly throughout the day and it has a calming effect. These past few days have felt good. Observing the breath before sleep has made it easier to fall asleep.
FWIW, the verses also mention that, as far as being serene is concerned, pranayama is a short term solution to a long term problem (and the gist of Upadesa Sara is on the long term solution but I digress).