Much of this is common sense, but the internet if full of videos of people getting hurt using axes. Some are funny; others not so much. Axes are dangerous tools and must be treated as such. When using an axe leather gloves, long pants, leather boots and eye protection are recommended to protect against the sharp bit and flying wood chips and splinters. It is also a good idea to keep a first aid kit available just in case anything does go wrong.
A few old school videos: