I think the most important thing that people who are not generally preppers can do is to think about what are the most likely things that may happen in their area (floods, power outtages, extreme heat, cut off by snow, terrorism or other physical attacks, strikes by public transport or other public services, etc) in the short term and how to respond, and also look at longer term trends and change how they do things slowly to be ready for those changes (moving away from diesel cars, changes to diets because of crop failures or reduced harvests of certain crops/animals, needing more renewable energy or being prepared for droughts etc).
Then think about what you need in your personal circumstances (3 days of water for everyone in the house, heat sources, light sources, first aid and medication, food for 3 days, etc) and start to make sure you have those things somewhere in the house - you can start to assemble a "kit" if you like, but even knowing you have things and where they are (and maybe putting that on a list in case others need to manage it if you're not there) is a big start. And also think about what you might need if you need to leave home in a hurry (whether for a hospital stay after an accident or a flood rushing at your house). I mean think initially - so you have a plan and know what you should get and where it is. Building an actual "bug-out-bag" (BOB) to grab and run is another step beyond that.
Lots of "emergency stores" are actually everyday things you already have, just making sure you have a baseline amount of certain things and not letting those go to empty before buying more. You might have candles and proper holders for dinner parties, or torches or solar lanterns for camping or garden events. You might already have a BBQ or camping stove that you can use as emergency cooking option. Sleeping bags can be good to snuggle under if the power is off or you need a BOB . Or you may have a hot water bottle for winter bedtimes to use under the sleeping bag reading a book in a power outage in winter, or flask for picnics to put hot water (once you've made the cup of tea or hot water for pasta) from the hot kettle to use later for more tea or washing up or washing yourself or the hot water bottle etc.
There's no need for panic. Just thinking about what could happen and how to be ready to look after yourself for a couple of days until public services can manage the situation and have dealt with those most in need.