This may seem obvious to some but make sure to read the owners manual. Every chainsaw is different and knowing how yours works can never be a bad thing.
Always wear protective gear. You will need gloves, a hard hat and goggles at the very least. A protective nylon vest is also a good investment as if the chainsaw ends up going through it it will sbe clogged up by the fibres and stop working.
Don't just jump into a large project. Start off small with a smaller tree or maybe firewood before attempting to tackle something bigger. Make sure that if you are a beginner do no use the chainsaw when alone. Having someone nearby could be a lifesaver if anything goes wrong. You could also keep a first aid kit nearby.
Never cut wood held by someone else. Always hold a running chainsaw with two hands. Dont rush, its better to wait and make a plan if you're unsure of what to do next than to rush through it. If you cut using the tip of your chainsaw you may experience kickback. this is very bad and can cause the chainsaw to come flying towards you. Use a scabbard to transport your chainsaw and keep out of reach of children.