Usage patterns
火事になるfor a fire to break out
A fire broke out because of a carelessly discarded cigarette.
火事が起きるfor a fire to occur
A fire broke out in the neighborhood in the middle of the night.
火事を消すto put out a fire
The firefighters put out the fire.
火事に遭うto be caught up in a fire
Last year, the house next door was caught in a fire.
火事を出すto cause a fire (in one's own building)
The factory caused a fire, and it turned into a huge commotion.
Expressions
対岸の火事someone else's problem; fire on the opposite shore 屁と火事はもとから騒ぐthe one who smelt it dealt it; the originator of a problem often complains loudest