I did yoga for 35 years. One of the breathing techniques I learned to calm myself goes like this:
Lie down or sit comfortably and close your eyes. Keep an open posture (don't cross your legs or arms). Start taking deep breaths and breathe in and out slowly. Breathe in to a count of 8, hold your breath for a count of 4, and breathe out to a count of 8. Do it over and over again for as long as you like. Try to breathe more and more slowly and take deeper and deeper breaths. (this can be a challenge if you have asthma like I do). Concentrate on the breath entering and leaving your body, and the counting. Try not to think about anything but your breath and your counting. (this can be very hard when you're manic, but the counting helps to keep your mind busy).

I also use what is called in yoga "alternate nostril" breathing with the same count structure, but it's hard to explain.
I can usually go to sleep when I remember to do this technique:
Use your thumb and forefinger to open and close your nostrils for this technique. Hold your right nostril closed. Inhale through your left nostril to a count of 8. Close the left nostril so that both nostrils are closed and hold to a count of 4. Open your right nostril and exhale to a count of 8. Repeat on the other side. (breathe in through the right, hold, exhale through the left) and so on. It sounds really weird but it's very calming. If you start to yawn, that's ok, just try to bring yourself back to the rhythmic breathing.