Sometimes seeing the new moon is not that hard. When the moon is far enough from the sun (30hours old), It stays long in the sky after sunset. Seeing the moon at or even before sunset is still hard, but twenty minutes later it will be very easy to spot it.
So was the new moon of April 30th 2014. I first saw it from Israel at 19:18 just a little before local sunset, and I immediately took photos. It was hard to focus since the moon was very faint. The difference between proper focus and improper are noticeable. Also if you search for the new moon with a binoculars, the focus is critical otherwise the thin crescent will not be seen
Out of focus new moon
New moon in focus
Even in a new moon, you can notice the red moon phenomena, but not as easy as with a full moon. The reasons are the same but since the moon is so thin, it will not be possible to see it in the eye at all some minutes before moonset. However a long exposure with the camera caught that photo at 20:30 just seconds before the moon disappeared behind the buildings (moonset was at 20:36)
ירח חדש בשקיעה
I also photographed many photos to create a time-lapse of 1 hour in just 30 seconds. The interval between photos is about 20seconds. Watch on full screen with HD quality and enjoy.