A few seconds. I only have to change my alarm clock and my watch. Everything else (cars, computers, cells) sets its own clock.
Every clock in my house changed itself except one, which I just noticed was unchanged yesterday. I don’t own any watches, just all our cell phones, and they did the work for me too!
So I reckon maybe two minutes.
My cellphone and both computers changed automatically (though one of the computers changed on the wrong date, so I had to remember to ignore it for the past week), and I haven’t bothered setting a time at all on my microwave since a power outage a year or two ago. That just left my alarm clock and my wristwatch, and the watch I was able to do while I was just standing around waiting for something, so it didn’t really cost any time. The alarm clock took no longer to do than it does to change the alarm, which I do a few times a week anyway.
Since virtually the only clocks I ever look at in my house are on my computers and cable boxes and they change themselves, to date the only things I’ve changed are my oven, my microwave, my car, and my watch (just did, thanks to this thread reminding me). Total time spent: about 1 minute, maybe two (my watch has both digital and analog faces and in spite of what it shows in the movie, changing one does not change the other).
I deliberately don’t like all of my clocks to change. While I don’t like DST much, I find a certain comfort in actually changing the clocks, I’ve noticed. But it couldn’t take me more than ten minutes, and we have a decent amount of clocks:
Both computers change themselves
Watch
Living room clock
Bedroom clock
Kitchen clock
I never set the microwave either, for the same reason as WhyNot - it goes off at the merest hint of a power failure.
Then I come to work and reset three more, plus the phones here. 
I didn’t waste a second changing my clocks. It took a minute or two (each) to change my alarm clock & wristwatch. Plus the timer on the coffee pot. (I ignored the stove–I’ve got a nifty little timer that works for cooking.) My PC, cell phone & cable box are automatic.
But this was time I spent–not wasted. I leave for work early & appreciate not having to do so when it’s darker than Dick Cheney’s heart…
About fifteen minutes to go around the house and reset the ones that need resetting.
Amusingly, the digital timer for the front porch light reset the time of day automatically, but it still needed the on and off times adjusted so the light can turn on before it’s dark outside.
When I was a kid my mother turned the clocks the wrong way and dropped me off at school 2 hours early.
None at all because I don’t change them in the first place. I get a perverse thrill out of telling everyone who tells me my computer clock is wrong that it’s their computer clock that’s wrong.
I’m always afraid I’m going to do this! “Spring forward, fall back.”
And, speaking of spring, I notice a lot more people are grumpy about DST in the spring when we all **lose **an hour of sleep!
Let’s see:
Bedroom:
4 clocks, including a travel clock. 2 reset automatically
2 watches
Living room:
2 clocks
Postage meter for my home office
Thermostat
Computer reset automatically
Cell phone reset automatically
Kitchen:
1 clock, reset automatically, but I had to put it near an outside window for a few hours
Oven
Microwave oven
Stopwatch
Family room:
1 clock
DVD player reset automatically
Computer reset automatically
VCR didn’t.
2 PDAs that reset automatically as soon as I docked them with the computer
Answering machine, which I forgot about until just now
Office:
1 clock
Answering machine
Computer reset automatically
2 cameras
2 cars
And I just remembered that there’s a timer in the kitchen and a clock in my guest room that I forgot.
So by this count, I own at least 32 timekeeping devices, 10 of which are supposed to reset automatically. But three of these actually required some intervention on my part.
So I had to reset 22 clocks manually. And when I reset a clock, I usually try to make it precise to the second. So I set my watch then go around to the others and carefully synchronize them. It takes a couple of minutes for each. So I think it took at least 40 minutes Sunday morning, and that’s not including the answering machine and kitchen timer I just did, or the guest room clock I haven’t done yet.
Less than five minutes.
Doc Brown? Is that you?