The first thing is to get people to realize that there is a problem. In 2013, the most recent year for which I can easily find statistics, there were 33,169 deaths from firearms in the US (excluding deaths by "legal intervention," IE, cop). Almost 2/3 of those, 21,175, were suicides. The MINORITY were the attention-grabbing mass killings like what happened in Oregon.
Honestly, the first part of a solution would be to get Wayne LaPierre out. He has led the NRA in a disastrous and radical direction since the early 90's, although they have been pretty rough since the mid-late 70's.
As far as safety issues, common sense solutions: A "loaded" flag, so that you know if there is a round chambered. Chamber locks, trigger locks, smart guns. There are many ways to make guns safer AND THE NRA OPPOSES THEM.
Yes, education, but the mandatory education which has been proposed upthread assumes that, A) Everyone wants to learn (and wants their kids to learn) about guns, and B) we live in a fully armed society where we need to learn about guns.
Yes, waiting periods. Especially for handguns, honestly. Again, these are the weapons most commonly used in suicides and "crimes of passion," and, generally, if you can get people to wait 72 hours, they won't go thru with it.
Maybe if the NRA and the gun fondlers would agree to reasonable steps, there wouldn't be need for unreasonable ones.