That's total bullshit there isn't a gun problem in the US. Keep telling yourself that. Just look around the world at other industrial, western nations and study the firearm death/murder numbers. It's crazy for you to think that, or it just proves that you - among many others - live entirely in a vacuum.
Really, not much at all. Just tighten up current gun laws, from who gets to buy them, to how long it takes, to what type of background checks are involved. Get rid of military-style automatic weapons, or significantly reduce access to them. Legitimate gun owners would have no issues keeping and purchasing guns as they wish. But it shouldn't be as easy as buying a friggin' scoop of ice cream. Reduce access to guns, clamp down on black market, gun show sales, do a buy-back program like they had in Australia and try to get lowlife bums to sell off some of their weapons. Not even sure it would work, but at this stage, with as many mass shootings that have taken place, it's worth a try.