Nauli is considered an advanced yoga practice. In this case, “advanced” means there is some risk of injury if nauli is not performed properly. Shandor Remete says that :
“The practice of nauli cannot be learned from books. One needs to work with a teacher who has mastered it and clearly understands its function.”
Of course, the task of finding, and recognizing, such a teacher is left as an exercise for the student.
B.K.S. Iyengar, in his book Light On Yoga, says about nauli :
“Care should be observed in its performance, otherwise the process leads to numerous diseases. It is not, therefore, recommended for the average practitioner. First master uddiyana bandha before attempting nauli….”
Despite Iyengar’s rather ominous warning, he provides no details as to the “diseases” caused by improper performance of nauli.
In a modern textbook, Yogani points out that :
“…if nauli is practiced over a period of time without the benefit of the purification practices of meditation and spinal breathing, it could lead to energy imbalances in the body.”
While it would be preferable to learn nauli from an experienced practitioner, it is not always possible to find one. People can, and do, learn nauli on their own. If one works slowly and with careful attention to the breath, as they would with any new yoga technique or asana, problems should be avoided. Pregnant women and people with heart disease or gastrointestinal illnesses should seek professional counsel before performing nauli. Practicing nauli should never cause physical pain of any kind although there may be some physical discomfort when first learning uddiyana bandha contractions.
Learning nauli typically happens in stages:
Stage 1: learn uddiyana bandha. The student learns to activate and maintain uddiyana bandha. The student commences a regular practice of uddiyana bandha contractions (known as agnisara dhauti, or simply agnisara ).
Stage 2: attempt central nauli. After practicing Stage 1 for some time (weeks or months, most likely), the student occasionally attempts central nauli. Eventually, central nauli is attained.
Stage 3: attempt right and left nauli. After central nauli is attained, the student, continuing their regular uddiyana bandha contractions and central nauli work, attempts right and left nauli.
Stage 4: nauli. Once right and left nauli are attained separately, the student can attempt to roll the abdominal muscles from right to left, and left to right.
Preparation: It’s very important when attempting any of these exercises to do so on an empty stomach. Five hours after eating is a reasonable minimum, but practicing first thing in the morning is a better idea. Also, evacuate your bowels before starting. 
1) Stand with the feet a bit more than hip width apart.
2) Bend the knees slightly and place your hands on top of the front thighs above the knee.
3) Exhale all of your breath out. Some instructions say to “quickly” or “forcibly” exhale, but exhaling in a relaxed fashion works fine . Make sure your abdominals are relaxed as possible once all of your breathe has been exhaled.
4) With your breathe fully exhaled, raise the rib cage and then concave the area below the navel upward and inward back toward the spine. Draw the lower belly in and up toward the spine allowing the lower back to gently round while the pelvis tucks under a bit. Hold this contraction for a few seconds, or as long as comfortable.
5) Release the contraction and then inhale through the nose slowly. If you gasp for air, you held the contraction too long.
Uddiyana Bandha Contractions
Uddiyana bandha contractions are simply the act of going in and out of uddiyana bandha repeatedly (also known as agnisara dhauti, or simply agnisara ). Follow the instructions above for Uddiyana Bandha. Once you’ve achieved the contraction in step #4, release the contraction without inhaling. Then re-establish the contraction (still without inhaling). That’s one contraction. Do as many contractions as you can manage comfortably. Then proceed to step #5 above.
Initially, you may find that you get out of breath quickly. Slowly build your daily practice until you can do 5-10 contractions without inhaling. You may eventually be able to contract and release 10 or more times without inhaling.
Do a few sets of uddiyana bandha contractions to warm-up your abdominal area. Follow steps #1-4 above to achieve an uddiyana bandha contraction. Then try to relax the middle of your abdominal muscles while keeping the side abdominal muscles engaged. Sometimes pressing a bit more firmly on your thighs with your hands helps. Don’t be discouraged if it doesn’t come easily.
Right and left nauli
Do central nauli a few times to warm-up your abdominal area. Then obtain uddiyana bandha and relax the left side abdominal muscles while keeping the right side muscles engaged. Sometimes putting more weight in the right side arm and leg helps. Now contract the left side muscles while keeping the right side relaxed. Again, putting more weight in the left side arm and leg can help.
Practice right and left side nauli a few times. Then try to move directly from contractions on one side to contractions on the other side. After a while, you will find that you can create a rolling motion from one side to the other and back. This is nauli.
Regular nauli practice: Once a regular nauli practice is attained, a typical session involves 500 to 1000 revolutions and requires from 15-25 minutes (depending on your speed), first practicing left to right, and then right to left . The number of revolutions per exhale may vary from just a few to as many as 25 (or possibly more) but the quality of the rotations should never be sacrificed for quantity . The speed of rotations is not important. It can be done either slowly or quickly and the same benefits will be derived.
Helpful videos and descriptions.
Yoga International Senior Editor Sandra Anderson offers her tips for doing nauli in this video.
This video shows a good view of the standing posture for nauli. Also, if you just watch the first 30 seconds, it shows the person doing uddiyana bandha (but not the release).
Teacher Adrian Cox demonstrates and discusses nauli in this video.
Teacher Larry Terkel demonstrates and discusses nauli in this video.
The AYP site has a rather long explanation of doing uddiyana and nauli.