This Video from Popular Mechanics is a good Primer on Generator Safety.
Providing Backup Power with a Generator.
There are three aspects of safety involving a Backup Home or Small Business Generator Safety.
Fuel Safety
Emissions Safety
Electrical Safety
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Fuel Safety
The Gas tank is almost always on top of the Generator. This allows for the generator to operate without a fuel pump. Most Generators use gravity to feed fuel to the generator making your generator simpler.
Airspace in the fuel tank, most manufacturers require that you do not fully fill the gas tank. Since the fuel will heat up during operation because it is above the motor the manufacturer needs to leave room for the fuel to expand as it heats up.
Fuel Spills, most tanks are designed so if you spill some fuel while refilling it will not drip onto the hot generator and cause a fire. If you do overfill or spill any fuel be sure to wipe it up before you operate the generator.
Portable Generator Emission Safety
The exhaust from the generator contains Carbon Monoxide. Be sure to point the exhaust away from any windows, doors or space you are going to be using.
Electrical Safety
If you are hooking your generator up directly to your residence or business it is very important to plug the generator in properly. Be sure your house is properly wired for the generator and you understand the controls.
Practice using your generator
Be sure test your generator regularly, several times per year.
Fuel Storage
Try using your generator for a day and actually see how much fuel per hour under normal usage it will burn. The estimates by the manufacturer can be off by a significant factor. Store and rotate at least a weeks worth of fuel for your generator. If you don't have fuel the generator is not going to work.