If there is any discomfort from the needles, it's usually only on insertion which lasts a few seconds. It is only the skin layer that contains the main pain receptors, and so just under the skin those receptors are not there. Threfore, the acupuncturist is aiming to place the needle just under the skin layer. When they do this successfully, there is no "pain" as such. You may feel other sensations like dullness, or tingling, but is not "pain" as we know it.

80-90% of people fall asleep on the table or go into a deep meditative state soon after the needles are placed.

Hopefully that helps clarify the process :)