I have a good amateur background in history and world politics, and went to university for both. I was also an infantryman with the 82nd Airborne, and did one tour each in Iraq and Afghanistan.
I plan to do nothing, other than observe events as they play out. The general structure of my reasoning is as follows: I live in a low-risk area; the probability of widespread violence is remote; the probability of organized, systematic violence more so. There are a few details of my baseline lifestyle worth considering: one, I don't own any weapons; two, I have a kitchen pantry which we keep stocked as a matter of convenience to last for a week before our lifestyle will even be affected, and with rationing could easily last much longer.
The most probable outcome by a long shot is that nothing happens and power transitions more or less as normal (excluding the customary rules of decorum). That isn't really an interesting case, but I put it to you that even if we assume the President refuses to leave office by declaring the election fraudulent or the like, the chances of violence affecting you are remote.
My first reason is straightforward: no enemies around. Most of the American population lives in ideologically-sorted zones, which is to say overwhelmingly-Biden areas or overwhelmingly-Trump areas. In order for there to be serious widespread violence, there needs to be someone around with whom to be violent; most of the time there won't be.
My second reason is that there isn't any organized plan to drive the violence. We can set aside the its-obviously-insane argument and instead consider that this would represent an entirely uncharacteristic amount of competence and concentration from the administration. Conspiracies of that type are very difficult to pull off, even for dedicated professionals, and this administration has had a tendentious relationship with seemingly everyone who meets that description in government.
My third reason is that even in the case where the administration makes active calls for violence, American civilization lacks the group structure by which to prosecute it en masse. In places like Iraq and Afghanistan, civil war can be sustained indefinitely; this is because of the family/clan structures around which life is arranged, and through which most activity happens (including the everyday things like agriculture and commerce). There is nothing like this in the United States; all of our coordination mechanisms are pretty specific to their intended function and by design are either tenuous (like employment) or to allow for other coordination mechanisms to fit into your life (school, church, sports fans). American civilian life does not have any equivalent of the total loyalty required to sustain violence over long periods of time.
In conclusion this means that if violence arises it will likely be spontaneous, short lived, and in areas that are contested or recently saw other violence (bad riots, for example).
I will take the trouble to recommend specifically against buying weapons for fear of nonspecific badness happening soon. Firearms are one of those things where training and experience is necessary both for getting utility and for reducing risk; it is easy to get proficient in marksmanship and maintenance, but very hard to practice handling under extreme stress. Further, if you are feeling motivated by general fears you or those around you are probably also susceptible to despair. You do not want to shoot a bystander by mistake, or accidentally give someone close to you an easy out at the wrong moment.
What to do instead: community hard. If you are by yourself, liberally abuse your communication options to check up on friends and family. Consider checking on your neighbors, especially if there's a power outage or something. Get some basics in, like hospitality and small celebrations. Sustain as many of your routines as safety permits.