The preferred method seems to be shooting them, but if they haven’t conveniently left any guns lying around the house, there are several other time honored methods.
The oldest one in recorded history is a knife, and throughout time, poison has remained at the top of the list. The safest way is to convince your sibling to do it, or hire someone.
One of the harder, less reliable ways is to turn the gas on the stove, and then turn up the hot water heater flame, but modern hot water heaters don’t have flames anymore. Another is the old “heater fell over” trick, as long as you make sure to pile flamable clothes under it first. Or you could try the electric appliance in the bathtub, but that require chosing only one to do without.
I have read of tampering with the brakes on the car, and in one TV show, the killer trained a dog to attack and kill.