Regular inspection of your chainsaw should be the starting point of your safety routine. There are elements and components of your chainsaw that should be checked before every use and others that should be checked on a regular basis whether you are using it regularly or not.
Engine - make sure you inspect the engine,
Spark Plugs - just like in a car, you should check your spark plugs regularly; faulty or worn out spark plugs are responsible for a large proportion of starting problems so keep an eye on them, at least once a week. (See also Why Won’t My Chainsaw Start? in the 'Getting Going' category)
Chain - as mentioned elsewhere it is vital to make sure the chain is free running and at the right tension the chain, the bar and any safety features like chain brake.
Controls - check all the controls like the throttle and clutch as well as the clutch drum to make sure they are not overwork and are working properly and make sure there is no dust gathering that might get into any working parts.
Safety Features - check and clean your chain Brake and give it at least one trial run before every use. Take a look at your Chain Catcher and check it for wear. Check all your Hand Guards and Handles and make sure they are stable and solid. For more information on safety features, click here - Chainsaw Safety Features
All these elements, parts and components will be clearly labelled in the manual and many chainsaw manufacturers will have itemised their own maintenance tips. Always follow these when they are included.