There are many pre-existing campaign settings for D&D: Greyhawk, Dragonlance, Ebberon, Dark Sun, Theros, Ixilan, Ravnica, and Ravenloft among them. My default is typically Forgotten Realms (I’ll perhaps get into why at a later date), and many campaigns take place there.
As DM, you may or may not want to adopt the standard measurements of time for the setting, or use conventional time, but if you’re going for an immersive experience, I recommend that you at least attempt to familiarize yourself with the calendar system of the realms: The Calendar of Harptos.
Week Tenday
Forgotten Realms does not use the conventional week. Instead, the standar grouping of days is called a tenday, and is comprised of (that’s right, you’re so clever!) ten days.
These days do not have special names (like Monday or Thursday), but are instead simply numbered (first day, second day…ninth day, tenth day) according to their position in the tenday cycle.
Months and Years
A month is made up of three tendays, which are also called rides. There are twelve months in a year, which also has five annual holidays and one leap year (or quadrennial) holiday to make up the difference. Conveniently, Toril has the same length of solar year as Earth, which I find considerate.
Years are counted using “Dale Reckoning”, which begins with “1 DR”, which was the year that the Standing Stone of the Dalelands was raised by the local humans and elves. Years preceding this event are referred to as “before Dale Reckoning” and are marked with a minus sign (-) and a year designation, much the same that we would use “AD” or “CE”, and “BC” or “BCE”.
There are other system of reckoning years, specific to various lands, but the one that you will encounter most frequently is Dale Reckoning.
Annual Holidays
Holidays never take place during a month, but always between months.
Midwinter is effectively the same as the winter solstice (translating to December 21 in the conventional calendar).
Greengrass marks the beginning of Spring, corresponding with the Spring Equinox.
Midsummer stands in opposite Midwinter, celebrating the middle of summer weather.
Highharvestide celebrates the harvest, taking place before frost (in most places) touches the ground but after most crops are ripe.
The Feast of the Moon is similar to a Day of the Dead, All Saints Day, or similar custom, celebrating ancestors, honouring the dead, and paying respects to the recently deceased.
Shieldmeet is a quadrennial (that means it happens every four years) holiday celebrated the day after Midsummer.
This is not to say that a land, nation, city, or other locale might not have its own special days. These are simply the ones that define the calendar year.
Hours and Minutes
Hours should be tracked (hypothetically) using an older system than conventional time. Historically, time was measured using three primary markers: dawn, midday, and dusk, with the night split using midnight. So, 2pm would look like “midafternoon”, 7pm might be “shortly after dusk”, and 3am could be either “a few hours after midnight” or “the beginning of the third watch” (if you use a three hour watch, four watch night system).
Personally, I typically use conventional time, even though it’s not historically accurate, because it’s a lot simpler to track it that way and easier not having to teach ancient timekeeping to all of my players.
More Information
This is a fairly concise look at the calendar of Harptos and Dale Reckoning. You can find the calendar in the Dungeons & Dragons Dungeon Master’s Guide 
