First, the government has already come for our guns. If you believe that the Second Amendment intended to safeguard the people's right to own arms capable of resisting government tyranny, then the government has already confiscated (or at least made it nearly impossible to obtain) the most useful weapons in the 1930s when the National Firearms Act was passed. World War I unmistakably demonstrated that the era of massed riflemen was over, and that explosives (however projected or directed at a target), large caliber cannon, and machine guns would rule future battlefields. (The importance of aircraft was not as clear at that point, but became apparent within the next decade). And so the National Firearms Act was born to make sure civilians could not own those types of weapons. And by the time inflation had eaten away at the cost of licensing an automatic weapon in the late 1980s, the law was amended to prohibit the manufacture of new automatic weapons for sale to the public. Most of our Second Amendment rights were eliminated long before most of us were born.
As for the remaining weapons, the answer is that it will proceed just as it has been done in the past. Such weapons will be outlawed slowly--in the name of public safety and controlling crime, of course--or ownership will require onerous fees or licensing process.
Example: Hey, everyone should have to take a $300 dollar safety class before they get a firearm. That is reasonable. And don't forget the licensing fee and the fingerprinting fee. And your ex- needs to sign off....There will be the occasional small sprints forward, such as banning a whole class of firearms (for example, assault weapons, "Saturday Night Specials"), but overall it will be a creeping ban.
And when it is illegal to own firearms (or a class of firearms), people will either turn in the weapons, or hide them for fear of confiscation. They certainly won't use them.
Raids will be made on occasion to make sure that those weapons still hidden will remain unused and hidden. Of course, the raids will be against a "bad" person: a drug user, a person with a history of mental problems, someone with a restraining order against him or her, someone selling unpasteurized milk, raising rabbits for meat, or perhaps in the course of a search based on some other pretext. (If you own a banned firearm, you are by definition a "bad" person). The point is that the raids don't necessarily need to be based on or conducted for the purpose of arresting someone for possession of the banned weapons, but through raids or searches for firearms or other reasons, there will be a fairly constant, albeit, small number of arrests and prosecutions for possessing banned firearms. And a trickle of arrests for possessing the banned firearms will tend to keep the sheep in their place.
The government will also outlaw or make it onerous to buy other things needed for shooting. Background checks and taxes or outright bans on ammunition. Bans on magazines. Bans on lead. Hazardous materials fees on gun powder. Limits on the quantity of ammunition or components that a person may own, store, or buy.
Example: You know lead is toxic, right? No more casting bullets unless you pay a fee, obtain a license, and put in ventilation hoods.And, of course, don't forget the social stigma that will amass against owning or using a firearm.
Example: Only a criminal needs a gun, right? Only a cruel person would hunt Bambi, right?It will be piecemeal and never enough to spark general outrage.
It has been facilitated by indifference (e.g., the attitude that I'm a hunter, so I don't care about a ban on military firearms, or handguns) and wanting to compromise (e.g., we should consider common sense restrictions, or engage in dialog). The way to stop it is to be politically engaged and have an attitude of no compromise, ever.
(Update: 6/1/2016: minor correction).