This begins with anecdotes, but ends with citations.

Both of my children (I am the father) were born via waterbirth and using hypnobirthing. The premise behind the waterbirth is largely analgesic: resting in warm water simply makes the experience more comfortable for mother. Changing positions requires less effort, and buoyancy makes for less skeletal muscular work once gravity is taken out of the equation.

Hypnobirthing deals with the "fear" aspect. It is likely that no other animal understands in advance what to "expect" from childbirth. Humans, on the other hand, have access to a vast amount of knowledge, mostly about the worst-case scenarios. There are numerous instances of women in comas giving birth (examples), indicating that no conscious effort is needed to give birth. In fact, the entire process is largely automatic.

However, the "fear" response appears to hinder natural childbirth. Women with a higher fear rating generally have higher rates of complications, and obstetric management is based largely on antiquated patient management research from the 50's and 60's. The topic of viewing childbirth as a "patient management" scenario is discussed at length here, and the author's review of this topic is based solely on peer-reviewed literature from the obstetric and psychology research community.

Back to the anecdote: by maintaining a heightened sense of relaxation through meditation, my wife was successful at delivering both of our children without medications, external procedures, or distress. You can learn more here, and watch for yourself on Youtube.