During amniocentesis do they stick the needle in the sac more than once?

Not usually. When having an amniocentesis we use ultrasound to help us guide the needle into the correct area. Of course you have to consider experience when having an amniocentesis done. A physician with experience usually can perform an amniocentesis with one puncture.
Just once. Once is all that is needed, and it's usually done with ultrasound guidance. Occasionally a second puncture may be needed if multiple sacs (twins, triplets, etc) but even then it can usually be avoided.