Equestrians follow a lunisolar calendar: the year is determined by rotations of the sun, while the months are determined by the rotations of the moon.
There are three calendar eras: Common Era (CE), Before Common Era (BCE), and Ancient Era (AE). The year that Princess Luna returns to Equestria is 872 CE. History classes will typically only cover events that take place in CE. Ponies pursuing a career as a historian or with a great interest in such things may find scattered information in BCE, but it surprisingly sparse by comparison. Only the most devoted historians can find records from AE.
The months are named for their corresponding full moon, such as the Snow Moon or the Harvest Moon, which get their names from the seasonal events that typically occur during that month.
Fresh Moon: The first moon of the new year.
Snow Moon: The last month of snow.
Maple Moon: Maple trees are ready to be harvested for their sap.
Pink Moon: The first spring flowers bloom, covering Equestria in pink.
Flower Moon: All of the spring flowers are in bloom.
Strawberry Moon: Strawberries are ready to be picked.
Thunder Moon: Summer storms are at their peak occurrence.
Red Moon: As the seasons shift, the moon takes on a reddish hue.
Corn Moon: Corn is ready to be harvested.
Harvest Moon: Many autumnal crops are ready to be harvested.
Frost Moon: As the seasons shift, the ground is covered in a light frost.
Dark Moon: The nights are at their longest, leaving most of the day in darkness.
The names of each day of the week developed and changed over time. The current system as it is known today has been around for roughly a thousand years.
Sunday — Sun’s Day: Day of worshiping the sun.
Monday — Moon’s Day: Day of worshiping the moon.
Tuesday — Two’s Day: Day to honor the Two Sisters. Youngest of the “day names”, was changed from Saisday (Seasons Day, Day of the seasons) after the ascension of Celestia and Luna.
Wednesday — Wedded Day: Day of joining the Days of the Alicorns with the Days of the Ponies.
Thursday — Thou’s Day: Day to celebrate “thou”, the Equestrian.
Friday — Free Day: Day of freedom from work. Traditionally, Friday and Saturday were the weekend, but during Celestia’s sole ruling of Equestria, Sunday shifted to part of the weekend to venerate her.
Saturday — Sated Day: Day of satiation from relaxation, as it was once the last day of the week and thus the end of the weekend.