It is important to wrap the tape on the threads the same direction that it will screw into the fitting so it doesn't get unrolled and bunched up.
As for using one or the other or both, that is what I've always heard, use one or the other, not both. I've always used just teflon tape on water lines and pipe dope on gas lines. So, I decided to do a little research and apparently it is just another one of those things where everyone has their way of doing it and they always have because the person who taught them did it that way.
There doesn't seem to be any downside or concensus that I could find here or on plumbing websites except that if you use both then put the tape first, which makes good sense to me. So, I am going to change my advice to this:
I prefer to use teflon tape only because it is neater and cleaner and always works fine. Or you can use a teflon based pipe dope. Or if you want to be extra cautious you can use teflon tape first and then a little pipe dope on top as an extra precaution.