I am a big fan of using calendars for my campaigns. It doesn't matter what kind of game I am running, from modern crime to ancient fantasy, I find calendars very useful for managing the flow of events, particularly when player characters or NPCs make plans and set things in motion. Calendars help you maintain consistency and breath a sense of realness to the setting. They can be daunting if you are not used to them, they can also lead you astray if you are not careful, but with a little bit of preparation and forethought they can serve you well.
The first thing to do when setting up a calendar is decide how the passage of time is handled in the campaign. If modern day, you can just grab a daytimer and you're good to go. If the setting is more fantastical or set in the future (or in the past) you may need to make some adjustments or create a custom calendar. For the sake of simplicity in my own campaign I try to cleave as closely to our own calendar as possible but you can have a lot of fun researching different calendars in history and tailoring an approach that reflects your world's history and its people. I kept our months but put the local name for the month in parenthesis. While days of the week appear on the calendar, the region where the campaign is set has no such convention, however these are still handy for communicating the passage of time to the players.
I use the calendar for several things. The first and most obvious is marking the passage of time. In my Swords of the Four Taverns Campaign, this became important as the party increasingly involved itself in politics and war. The second is tracking all the moving parts of the campaign. I needed to know how many weeks had passed since they started levying troops and how long it would be before that message they sent reached Eshmunazar. I also needed to track the plans of my NPCs and significant events in the region. By committing things to the calendar they stay consistent and fair.
My method is pretty simple. Each day that passes on the calendar is marked by circling the number. Any major event is written in blue or green and underlined if it involves the PCs in anyway. I use blue ink to write the actions and plans of NPCs, but green ink to write the actions and plans of PCs.
While it may be difficult to read if you look at the image of my calendar, you see that on the 11th it states "Rasimon sent to Vargus". This is because the players sent an assassin named Rasimon to kill Vargus, a Castle Lord who commands a large number of soldiers. On the 20th it states "Rasimon strikes at Vargus". This means that is the day Rasimon makes his attack against Vargus.
But the players themselves were also subject to an assassination attempt. On the 6th it states "Assassin arrives in Goff-Tel", on the 14th it states "Intended day of assassination". Because the players information network uncovered the assassin's presence before he could strike, they were able to deal with the threat prior to that date.
I also use the calendar to mark festivals and holidays. So on the 21st it states "Feast of Druza begins". This is an eight day feast that is mainly just setting backdrop (Druza was the prophet of one of the major gods worshipped in the region). But it could become important as either the players or their enemies might use the feast to their advantage.
You don't have to use this exact method. Perhaps two kinds of ink is a bit much for your needs, or maybe you need three or four colors of ink to distinguish different types of developments and events. Perhaps all you need is to mark the passage of each day. Personally I find it incredibly helpful. It is easy to forget when the players set a plan in motion and marking it on the calendar really makes that much easier to manage
What I like about keeping track of the passage of time in this way is it gives a sense of concreteness to the world. I am not just having festivals pop up out of nowhere or shooting from the hip when it comes to figuring out when a crucial message reaches the king.