Using a chainsaw is often seen as a hazardous activity at the best of times but if you use common sense and a few rules the chainsaw shouldn't be a dangerous tool.
Use protective clothing, etc In all circumstances you should wear a good set of gloves -- ideally specialist chainsaw gloves with a reinforced panel on the back of the hand. If you're using a chainsaw for more than a minute hearing protection should be mandatory. A hard hat should be worn and steel-toecapped boots. Leg protection (chaps or full trousers) should be worn if you plan to be cutting downwards. The Health and Safety Executive recommends that all chainsaw operators carry or wear a first aid kit, rather than relying on a first aid post some distance away. Your first aid kit should include a dressing suitable for large wounds -- chainsaw injuries aren't likely to be fixed by a plaster.
Don't put your body in the kickback arc. If the saw kicks back as it will do at some point, the tip of the chain bar will follow an arc whose centre is approximately at your left hand. If you hold the saw so that you are cutting downwards, with the blade in line with the centre of your body the tip of the blade will move towards your face if it kicks back. The way to use a chainsaw is to put the work between yourself and the blade. If you can't do that, stand well to the left of the arc.
Think about where the piece of wood will fall. Hopefully you aren't going to put any part of your body under something that will fall on you when it is cut, but you might be surprised how quick a heavy log rolls away from the trunk when it is cut. If it is possible, you should position yourself uphill from where the wood will fall.
The tree might not fall where you plan. Even if you cut the requisite hinge, there is always a chance that the tree will fall unpredictably. Practice makes perfect but the tree should be pulled in the direction you want it to fall. Generally you need ropes and pulleys for this.
Knowing the limits of your equipment should help keep you safe. And common sense will go a long way to keeping your chainsaw activity relatively safe.
