I bought a chainsaw when we moved to our current house, as the garden is mostly jungly hillside. When using it I am almost paranoid about safety, and always remember something written on a past STW chainsaw thread - "there's no such thing as a minor chainsaw injury".
The main thing I do is to check before every cut that there isn't something behind the branch I'm cutting, which the tip could come into contact with and cause a kick-back. And also, for every cut, run through the whole cut in your mind before you start and work out the flight path of the bar/chain if there is a kick-back. Then try to avoid having any body parts in that path... it's a slightly time-consuming process but time very well spent IMO.
I also spent a bit of time practising kick-back, that is to say, deliberately experiencing it in a controlled way so I know what it feels like and how it occurs. Search youtube, there are plenty of examples of how to do it
safely with the minimum amount of risk.