I don't think that anybody believes that the problem of mass killings can be solved. There have always been crazy, homicidal maniacs throughout human history, and there always will be in the future.
What we, as a society, should strive for would be to mitigate such incidents. If we can make the weapons of choice by the people who commit these crimes less destructive, then we've taken a step in the right direction. As I mentioned earlier, a mass killing of "only" 13 people, as horrible as that is, is still better than a mass killing of 26 people.
It's a complex issue that needs to be addressed from different sides. Being able to identify and treat/stop potential mass killers before they snap and carry out their plans is another approach. When you look at all these incidents over the past dozen years, from Columbine to Virginia Tech to Newtown, there's a somewhat common theme in the profile of the killers. That's a starting point.
And I also addressed the media's role in all of this, how the killers are sensationalized and long remembered after the fact. The media needs to understand and acknowledge their indirect role in fueling these incidents.
Finally, we need leaders who are interested in doing the right thing (whatever that may turn out to be), and not just the popular thing that panders to the wishes of their electorate or the lobbyists for the purpose of securing future votes or campaign contributions. Sadly, I have little to no hope for this last item..