Usually when I prep for a Dungeons and Dragons session, I have some vague idea of the direction I expect the session to go in. Often my players surprise me and things go completely off the rails (actually, usually that's the case), but I like having a few ideas up my sleeve of encounters they might have and things they may come across to fall back on. I find this also helps with the pacing of the adventure and stops my players getting too bogged down without any sense of direction - because if this happens, I always know the next story beat that can pop up at a moment's notice.
Sometimes, however, this isn't really possible. The last session may have ended at a point which doesn't give any clear indication of the direction the party will follow at the start of the next session, and trying to prep for every possibility in my usual way is overwhelming. At this point, I have a different style of prep that I fall back on - and often this leads to the most fun and unpredictable sessions.
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What in the world is going on?
In short, ask yourself just one question: what are all the other actors in the world (and by all, I really only mean the few factions or NPCs you already have mapped out) doing at this moment? You don't need to know what exactly they're going to do next or have the whole adventure planned - just an idea of where they are and what their intentions are at that moment in time.
Think about the different factions at play, what they want to achieve, and how they may plan on doing that. Even a couple of sentences here and there is enough to give you an idea of what they're planning. Then that's it, that's as much prep as you need - and you can weave these different elements into the session as you choose (and in a way that makes sense) depending on the choices your players make.
I'll give an example from when I ran The Lost Mine of Phandelver(*) as a single-player adventure with my partner. I assume most of you will have played this adventure - but spoiler alert in case you haven't. We were mid-way through the campaign, and the previous session had ended with my partner rescuing Gundren from Cragmaw Castle and fleeing into the surrounding forest with the unconscious drawf in a Bag of Holding.
This posed something of an issue, as I didn't know if she'd decide to head back to Phandalin, or on to the mountains and Wave Echo Cave, whether she'd want to return to Neverwinter, or try to meet up with any of a number of NPCs she'd made friends with throughout the adventure. No matter: I simply asked myself what the various other factions within the adventure were doing at the same time - and specifically, which of those she might run into within the course of the next session (i.e. which NPCs were nearby).
In the vicinity at the time were a number of the Cragmaw Goblins that had been lured outside by her NPC companion, the doppelganger Vyerith who had fled the castle following an altercation with King Grol, Iarno Albrek who had escaped from the Red Brand Hideout several sessions earlier and was secretly following my partner's character, and a band of Orcs who she had seen tracks of, but decided to avoid, a few sessions back.
I simply wrote a few sentences about each of these groups and what their intentions were, and that was it. Prep done.
When the session came around and my partner's character decided to head back to Phandalin to seek medical help for Gundren (who, thankfully, she remembered to take out of the Bag of Holding before he suffocated), it was easy enough to weave in an encounter around the campfire where Iarno Albreck arrived, disguised as a travelling apothecary, or when Vyerith showed up in the middle of the night attempting to steal back Gundren.
To all intents and purposes, this session seemed just as well prepared as all previous sessions - but in terms of prep time, I'd spent perhaps only 20% of the time that I normally would.
Another great thing about this prep method is it gives more agency to your players. Sometimes it's enough to prep a problem - but leave the solutions entirely up to your players. In a campaign that I'm running at the moment (a homebrew adventure in Ancient Greece) last session, my players were arriving at Knossos and needed to find a way into King Minos's palace.
I had a few ideas of ways they may try to sneak in - but rather than trying to railroad them in any particular direction, instead I just thought about which characters and places they might find in the city, and then left them to it. They came up with a solution I hadn't thought of, and everyone had a blast during the session. Not only can this prep style save you time, then - it also gives more creative license to your players. This is almost always a good thing.
One thing to note about this style of prep is that it keeps you as the DM on your toes. There's something exhilarating about starting a session without any real idea of where it's going to go. It also gives you great experience for thinking on your feet or improving your improv game. Not having anything planned out can certainly put you outside of your comfort zone - but I'd thoroughly recommend it. Next time you're prepping a session and you don't have a clear idea of where it's going to go - give this a try. Just think a little about what's happening in the world, and then let your players figure it out. I'm sure you won't be disappointed with what they come up with!