I do not kill rats; I am a peace loving, non violent, earth loving hippie! But in case you need to get rid of your rat problem there are a few methods that are commonly used. There are rat poisons that are available commercially. These are mostly arsenic based and result in most of the internal organs of the rat being cut, damaged and lacerated and ultimately resulting in death. They can be added to food items and left out for the vermin to feast on.
It is very essential to wear face masks and gloves to avoid coming in direct contact with the poison and making sure that humans and other animals do not consume the poison by mistake.
Another option is specially designed rat traps that work on the principle of a trap door triggered to bait. The bait is generally something that the rats eat, and where rats are concerned this includes everything we eat. Finally you could try the barbaric way and run after the rat with a hockey stick.

Rats once killed, especially by poison should be properly disposed off.