Deep diaphragmatic breathing is very relaxing, and doing so before bed can help one get a good night's sleep.  Here is a practice from the Himalayan Yoga Meditation Tradition that can help one fall asleep and often results in deeper and more restful sleep.

In order to do this practice properly, some proficiency at diaphragmatic belly breathing is required.  Here are instructions for two easy diaphragmatic breathing practices, that will teach you to breath this way. Once you can breath diaphragmatically, then you are ready to begin the sleep practice.

Here's the sleep practice:

Lie in bed on your back, and begin diaphragmatic belly breathing in the corpse posture (as taught  Here)  for one minute. Then, continuing to breathe diaphragmatically, start breathing so that the exhalation is twice as long as the inhalation.  In yoga, this is called 2:1 breathing.  Count the length of exhalation and inhalation seeking to exhale twice as long as you inhale.

Use an easy to accomplish count, such as exhaling to a count of 6 and inhaling to a count of 3, or exhaling 8 and inhaling 4. Your goal is to breathe in a relaxed way, smoothly and deeply, with exhalation twice as long as inhalation.  You are not trying to completely exhale nor completely inhale. 

Be aware of the sensation of the flow of the breath, and take care that the breath flows continuously without jerks, stops, or shakiness.  Pay special attention that there are no pauses between the exhalation and inhalation.

Breathe as follows:

8 breaths lying on your back
16 breaths lying on your right side
32 breaths lying on your left side

You may fall asleep before completing the exercise and this is fine.  This practice will often result in falling asleep and sleeping more deeply and with greater relaxation.

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This article is adapted from a practice set forth on page 197 of Freeom From Stress, by Dr. Phil Neurnberger, Himalayan Publishers.