The media exaggerates violence in our society today by giving violent events more coverage than other sorts of events that happen more frequently than violent events do. There's a well known local TV news saying "if it bleeds, it leads," with the idea being that a story with violence will go on the news right at the beginning. So the answer to the "how" part of your question is that they do it by putting the stories in more prominent parts of the newscast or newspaper and by running those stories for longer than other kinds of stories.
The reason for this is that people seem to prefer watching accounts of violence (and of disasters and things like that). These types of events seem way more interesting to the public than stories about good things happening. So the answer to the "why" is because viewers seem to prefer those stories and so media outlets that need to make a profit have to show them.
Because of this, we see more stories about violence than would be warranted by the amount of violence that actually occurs.
Some links: http://pediatrics.aappublications.org/cgi/content/full/113/6/1771#ABS (some stuff about how there's too much violence)
http://www.commercialappeal.com/news/2009/jun/10/tv-news-dealing-overdose-of (looks at both the issue of there being too much and the idea that it happens because of the need to make profit)