Some say that the Sanskrit word nauli means “to churn” . B.K.S. Iyengar says that “nau” means “boat” and “li” means “to cling to, lie on, or cover.” He notes that the “pitching of a boat on a stormy sea conveys some idea of the process of nauli.”  Other names for nauli are nauli kriya, lauliki, naulika, nyoli, and chalani. 
The earliest known reference to nauli is in The Hatha Yoga Pradipika, a 15th century yoga text written by an Indian yogi named Swatmarama . The book directs the yogi to (translated from the original Sanskrit):
“Lower the shoulders. Revolve the stomach left and right with the speed of a strong whirlpool. This is called Nauli by the masters. This Nauli is the crown of Hatha practices. It kindles a weak gastric fire, restores the digestion, always brings happiness, and dries up all defects and diseases.”
The Gheranda Samhita, a (probably) 18th century Sanskrit work, provides a shorter description of the technique . Translated from the original Sanskrit:
“Rotate the stomach quickly on both sides. This gets rid of all diseases and the bodily fire increases.”
Nauli is described or mentioned in many modern (20th Century) yoga texts, as well as various journals and magazines. This Google Book search returns around 5000 English language books and magazine mentioning the word nauli – there are a fair number of unusual results (duplicates, references to a person named Nauli, etc), hence the estimate of 5000 out of about 7100 returned results): Google Book Search.
Here is an annotated list of some references (in no particular order):
The Hatha Yoga Pradipika. Translated by Brian Dana Akers. YogaVidya.com, 2002. ISBN: 0971646619.
A recent translation of this classic work with attention given to the primary source material. Required reading.
The Gheranda Samhita. Translated by James Mallinson. YogaVidya.com, 2004. ISBN: 0971646635.
Another modern translation from the YogaVidya catalogue. Refined and valuable.
Light On Yoga. B.K.S. Iyengar. Published by Schocken Books, revised edition, 1995.
Perhaps the definitive modern asana reference. Iyengar describes uddiyana bandha and nauli in the section “Bandha and Kriya,” pages 425-428.
Hathatatvakaumudi. Translated by Dr. M.L. Gharote. Published by The Lonavla Yoga Institute, 2007. ISBN: 819016175X.
A treatise on hatha yoga written by an ayurvedic practitioner named Sundaradeva, probably in the 1700’s. Hathatatvakaumudi means “light on the principles of hatha yoga”. Nauli is described on pages 106-108.
Hatharatnavali. Translated by Dr. M.L. Gharote. Published by The Lonavla Yoga Institute, 2002. ISBN: 8190117696.
Yet another treatise on hatha yoga written by a scholar named Srinivasa, probably in the late 1600’s. Two types of nauli are mentioned (internal and external) though it’s not clear what the difference is between the two. Page 16.
Satkarmasangrahah. Translated by Dr. R.G. Harshe. Published by Yoga-Mimamsa Prakasana, Kaivalyadhama, 1970. Amazon.com ASIN: B0006CNQF8.
Written by Cidghananandanatha, this short text mentions three types of nauli: Bahya nauli, Nalanauli, and Antranauli. Pages 39-40.
Shadow Yoga, Chaya Yoga. Shandor Remete. Published by Shadow Yoga, 2006. ISBN: 0977539008. [Also, revised edition, 2010. ISBN: 1556438761].
Remete offers a short chapter on nauli which he calls ” …the bridging point between asana and pranayama…”
Hatha Yoga. Theos Bernard. Publisher: Essence of Health, South Africa, 2001. ISBN: 0958446016.
Originally written as his Ph.d dissertation for Columbia University in 1943, this classic work discusses uddiyana bandha and nauli with numerous footnotes.
Advanced Yoga Practices: Easy Lessons for Ecstatic Living. Yogani. AYP Publishing, 2004. ISBN: 0976465507.
One of the better modern texts that teaches uddiyana and nauli. Nauli is discussed on pages 208-211.
Heaven Lies Within Us. Theos Bernard. Publisher: Essence of Health, South Africa, 2002. ISBN: 0958446113.
Bernard’s autobiographical account of learning yoga. Originally published in 1939. He describes learning nauli as well as other yogic techniques.
The Yoga Tradition. Georg Feuerstein. Hohm Press, 2008, 3rd edition. ISBN: 1890772186
Feuerstein offers barely 1/5 of a page to nauli, but he provides hundreds of pages of history and background material on the various cultures that spawned the yogic sciences.
Yoga in modern India: the body between science and philosophy. Joseph S. Alter. Princeton University Press, 2004. ISBN: 0691118744.
This book looks at, among other things, some of the medical research about nauli from the early to mid-20th century.
 Yogani, “Advanced Yoga Practices: Easy Lessons for Ecstatic Living”. AYP Publishing, 2004. ISBN: 0976465507. Page 494.
 Remete, Shandor. “Shadow Yoga, Chaya Yoga”. Published by Shadow Yoga, 2006. ISBN: 0977539008. Pages 68-69.
 “The Hatha Yoga Pradipika”. Translated by Brian Dana Akers. YogaVidya.com, 2002. ISBN: 0971646619. Page 41.
 “The Gheranda Samhita”. Translated by James Mallinson. YogaVidya.com, 2004. ISBN: 0971646635. Page 13.
 Daniélou, Alain. “Yoga: Mastering the Secrets of Matter and the Universe”. Published by Inner Traditions, 1991. ISBN: 0892813016. Page 64.
 Iyengar, B.K.S., “Light On Yoga,” Published by Schocken Books, revised edition, 1995. ISBN: 0805210318. Page 427.