This breathing exercise done just before sleep time has helped me sleep better: 5 minutes of even breathing, each breath consisting of a 3-second inhalation and 6-second exhalation. You want to exhale about the same volume of air you inhale, so you should exhale more slowly than you inhale. If 3-6 seconds is too long for you, begin with 2-4 seconds (2 seconds inhale, 4 seconds exhale). It helps to have a metronome app to time your breathing.
This method is discussed in "Anatomy of Hatha Yoga" by David Coulter, Chapter 2. Why does this work? I quote from this book (page 91): "This connection between heart rate and breathing, known as respiratory sinus arrhythmia, ... causes the heart to beat more slowly during exhalation than it does in inhalation. ... If you take longer to exhale than to inhale, especially when you are relaxing, the slowing-down effect of exhalation will predominate."
This method is discussed in "Anatomy of Hatha Yoga" by David Coulter, Chapter 2. Why does this work? I quote from this book (page 91): "This connection between heart rate and breathing, known as respiratory sinus arrhythmia, ... causes the heart to beat more slowly during exhalation than it does in inhalation. ... If you take longer to exhale than to inhale, especially when you are relaxing, the slowing-down effect of exhalation will predominate."