How I run Downtime and the Calendar:
What is downtime?
Downtime is what happens between sessions of D&D. For example, between two recent sessions, one of my players spent his downtime buying powdered diamonds, and building a collapsable scaffold so that he could cast multiple glyphs of warding (essentially D&D landmines that only are triggered by a particular creature or creature type) to set a massive explosive trap for an Aboleth in the sewers of Waterdeep. Downtime gives the players freedom to pursue their own sidegoals, and flesh out their characters, without taking up time when everyone is sitting down to play the actual campaign.
Downtime ALSO allows the WORLD to change, adapt, and react to the actions of the players. So for example, early in the campaign, the players spent a few sessions delving into a crypt in the City of the Dead (a cross between Central Park and a cemetery--probably best avoided at night, you might run into the crazy bird lady from Home Alone 2). This particular crypt is owned by a vampire, "the Baron of Blood." And he didn't much like the fact that a bunch of adventurers kept delving into his tomb, setting off traps, and killing his monsters. So during HIS downtime, each week, he spent time hiring mercenaries to guard the entrance (the players ended up overbidding and hiring these mercenaries--one of whom became a PC, lol). He also spent time resetting traps, trying to bolster his defenses, and marshall his forces to keep the PCs away. Eventually, the Baron decided that the best way to deter the PCs from continuing to enter his tomb ever week would be to hire the PCs to go after other monsters who were encroaching on his territory. The barons strategy seems to be paying off well, since the players have mostly left him alone (aside from collecting bounties) for the last two months.
How does Downtime work?
Well basically, downtime works like this. During a campaign session, players have some control over the flow of time. Players can spend their time, travelling, exploring, fighting monsters, resting to regain spells, or in one recent session, my players spent an entire week of in-game time casting glyphs of warding to lay their aboleth trap in the sewers.
However when the game is not "IN-SESSION," players DON'T HAVE CONTROL over time. When the players aren't playing, the calendar of the campaign setting moves forward in synch with the real world calendar. For example, I am writing this on April 16, 2021. In my campaign, today is Tarsakh 16, 1493. In the real world, tomorrow will be April 17, 2021--and in Faerun, tomorrow will be Tarsakh 17.
The last time I ran a session of my Waterdeep Campaign was on April 13--so the campaign date was Tarsakh 13th. As I mentioned above, my players spent 5 days casting spells in the sewers. They also spent one day tracking down and killing "the Necromancer." So at the end of the last session, my players were on Tarsakh 19th. The real world calendar hasn't caught up with them yet. Our next campaign session is scheduled for April 20 (Tarsakh 20). So there isn't any problem with the timing--they just don't have any "downtime" to spend between sessions this week (Tarsakh 14 - 19) because they spent all of their time on that project in the sewers.
For the sake of example, and as an illustration, lets say that instead of waiting until next Tuesday, we decided that we were going to run another session in the Waterdeep campaign this Saturday (April/Tarsakh 17th). In that case, my players would NOT be able to use the same PCs they used on Tuesday--because those PCs spent Saturday setting an aboleth trap. Instead, they would have to use other PCs--either rolling fresh characters, or in this case, using other PCs from their stable (most of my players have two PCs currently. So for example, the guy who plays the Paladin Aoth, would have to play his back-up PC--an elf fighter named Forwyn.
Interestingly enough, Aoth started off as a one-off NPC guard who the Baron of Blood hired to try to keep the pesky adventurers out of his tomb--but Aoth was hired by the party, and the guy who plays Forwyn asked if he could use Aoth as a PC when Forwyn had to spend a month in hiding after committing a major crime in Waterdeep.
One change I've made to the Faerunian Calendar
There is a lot of "lore" in the Forgotten Realms setting. Including a bunch of information about the calendar as it works in the ""canonical"" version of the setting. Specificially, Faerun's calendar has 12 months of exactly 30 days--each of which is divided into three "tendays." These differences probably wouldn't matter to me much if I wasn't keeping my game calendar synched to the real world calendar.
But since I AM synching my game calendar with the real world calendar, I got rid of "ten days," and the months all have the same number of days as the equivalent month on Earth. So Tarsakh (April) has 30 days, while Ches (March) had 31 days, and Alturiak (February) had 28 days. If I wasn't running it this way, it would be harder to keep track of what day of the month it was--because it would differ slightly from the real-world Earth calendar I'm using to track it. It's not a deeply significant change, but it does conflict a bit with the "established lore" of Faerun (not that I care much).
I just mention it because I think it makes it a lot easier to keep your campaign calendar synched 1-to-1 with the real calendar by smoothing over differences like this.