I'm a new DM and I'm having trouble keeping track of the passing of time in my adventures.
How do you guys keep track of how much time passes and when?
Good question. That was a topic I had a tough time with in my early years of DMing. Only in the past 5 years have I really been able to master it. And it's really not that hard.
Basically, I have a clock on my desk and one across the room (on a microwave we have in our game room) when we play. A lot of out of combat game play has a ton of player interaction, both in character and out, and role-playing with NPCs. During those times I simply look at the clock every so often to see how much time has elapsed. I let my players know this, too, so there's no surprises. This helps a lot to track spell effects that last longer than the combat they were cast during. So, no "But my such and such spell should still be in effect."
Aside from that I keep a campaign world calender to track days and months on a game log I keep for each session. Before I start my games I just make a note of what the current date is. When we pass days during the game I just tick them off somewhere on the log.
Hope that helps.
Take notes; write down the passage of time.