I asked a similar question a year or so (on checking , two years!) about my first game. Lots of helpful advice, some of which was specific to the adventure (Storm King’s Thunder) I’m running, lots of which is either transferrable or global in applicability.
As a recent first time DM, things I’ve learned:
DND Beyond is a useful resource - I use it for character sheets, but also spell details, rules checking etc. that I need to reference in the moment - much easier than paging through the physical books.
Enjoyability of the session- particularly for me - is generally directly proportional to the amount of time I spend prepping. Happily, I have found I really enjoy the prepping. But it really makes a difference if I put in the time to make sure I know;
- NPCs motivations, appearance, likely response to the characters, likely response to other NPCs. I am a massive ham, so NPCs are a chance for me to try out different accents. For appearance, well worth searching for online images you can use, or using generative AI to bring people alive. . Same goes for monsters, a good pic of e.g. a rhemorraz (sp?) in full attack mode does a lot to set atmosphere.
- The map and locations (sounds like you’re on this) so I know where people should be going and what should be there. Again, you can find pretty cheaply some good images and maps of standard locations, e.g the warehouse district, dockside tavern etc. that will at least give you ideas.
- What each PC should be doing and how the players are going to find enjoyment. This is partly a mix of character strengths (i.e. if this is a diplomacy-and-stealth mission that suits the Rogue and the Bard, what are the Ranger and Fighter going to be doing? How do they contribute to the party’s success?) and player strengths (i.e. some like strategising, some like interactive role play, some like it when their character does something cool.)
- What’s the main line of this adventure, and what are the variations? What if their first plan fails and their deception is revealed? What if they don’t trust the guy they should trust? What if my daughter takes one look at the picture of the “friendly” bard I’d prepared and immediately declares him untrustworthy, thus screwing up a massive third act reveal the very first time I go off book to script my own session? Some of this you can just force (“Shut up kid”) but I like having an alternate route.
- What do I want people to feel during this session? “Not bored” is the baseline, but is this adventure suspenseful, exhilarating, funny, terrifying? Are we ending with a sense of triumph, relief or on a cliff-hanger?
- Plant some stuff for later. This can go two ways - if you know something big is going to happen in a couple of sessions time, try to foreshadow it by e.g. having an NPC mention in passing the important vote coming up soon, a bard sing a song of a presumed dead hero, a dead villain can have a trinket that will turn out to be more meaningful later etc. etc. Or just have this stuff happen anyhow and then build it in later.
Golden rule; keep looking round the table, if people aren’t having fun, switch things up.