Lots of bad advice in this thread. As a fellow mathematician who has taught intro stats before, and am currently teaching it (at a large research university) again this summer, here is my take:
1) Be prepared for the fact that many will not have taken a math class in many years, some 5 or more. They will recall little from their previous math classes other than intuition. Their arithmetic skills are poor. Be sure you are evaluating them on their understanding of the stats material, and be forgiving of arithmetic errors
2) They will be heterogeneous. Some will prefer abstract formulae, others will want to see things in words. Give both. Some will like to read the book, others will like lectures. I am linking to relevant Khan Academy videos on my website along with the date of the lecture they go along with. Anything you can do to come at things from various angles will increase the proportion of the class that understands it.
3) Try and explain the big picture. I am often motivating things with social science "experiments", or medical experiments. Find out what kinds of examples click with your students, and use those. While their arithmetic skills are often abysmal, they generally grasp quite readily the major ideas, how one should apply them, and when. They just get lost a bit in details.
4) Don't get bogged down teaching too much probability. It's an easy trap to fall in to.
5) Have fun. I've found teaching this course to be more work, but rewarding. A lot of these students have a near phobia of anything math, it's nice to see things clicking for them and them grasping the big ideas, if not the specific computations.
Okay, back to writing tomorrow's lecture...
P.S. Neither math nor statistics are "natural science", much less any kind of science.