This lesson is covered in more detail in Week 11 of Introduction to Sindarin

Amdiron: Mallú menathogir?
Ivrinel: Menim na vinuial abor. Harthon toled na Lothlorien ned Firith.
Siron: Dadwenatham ned laer!

Amdiron: What time will you go?
Ivrinel: We go at dawn tomorrow. I hope to come to Lothlorien in Fading.
Siron: We will return in summer!
Middle Earth has three main calendar systems: Shire Reckoning, used by the Hobbits; Rivendell Calendar, used by Elves; and the Steward's Reckoning or King's Reckoning, used by Men. As we are mortals, and as the Gondorians spoke Sindarin, this lesson will cover the systems of both Elves and Men.

Days of the week

The Elven day lasted from sunset to sunset, and their weeks lasted for six days. The Númenoreans altered this to a day from sunrise to sunrise, with a week of seven days (like our own).
Minuial = Dawn ('first twilight')
Aduial = Sunset ('second twilight')
Orgilion = 'Day of stars', 1st day of the week
Oranor = 'Day of the sun', 2nd day of the week
Orithil = 'Day of the moon', 3rd day of the week
Orgaladh* = 'Day of the tree', 4th day of the week
Ormenel = 'Heaven's day', 5th day of the week
Orbelain = 'Day of the Valar', 6th day of the week
*Older Elves would call this day Orgaladhad = 'Day of the two trees'.
Oraearon = 'Ocean's day' 7th day of the week

Lefenar = A week (originally of five days).
This is a very old word that dates back to when some of the Elves lived in Valinor. At this time, the week was five days long.
Odlad = A week (of seven days). This word is reconstructed on the basis Lefenar is unsuitable for weeks of more than five days.
Paenor = A fortnight (of ten days). This word is reconstructed.

Festivals and important days

The Elves appeared to have celebrated at least some of the solstices, also known today as the Wheel of the Year (8 equally spaced festivals that occur at the changing of the seasons and the equinoxes). Unfortunately if they celebrated any of the others we don't have names for them in Sindarin.
Nost Lyth (older Goldogrin 'Nost-na-Lothion') = Birth of Flowers. This was a festival known to be celebrated in Gondolin (probably heralding the arrival of Spring) but may still be celebrated.
Enedhinor = Middle day of the year (in Gondorian reckoning, the 183rd day of the year)
Amanor = Yule. This is the winter solstice that we celebrate today around 21st December.
Penninor = Last day of the year (20th March).
The exact dates of when different seasons would have started and ended are subject to debate and to a certain extent the changing of the years (when leap years are recorded and so on).
For a look into this problem, visit this site and have a look at their calendars and calculations.


Months and seasons

The Elven year began in spring, and ran for six seasons from spring to spring. Laer and Rhîw are 72 days long, and the other four seasons are 54 days long.
This calendar was changed by the Númenoreans so that the mortal year starts in midwinter (as ours does), and instead of six seasons, they split the year into twelve months. Ten months had 30 days, and the other two had 31.
Elven reckoning
Mininor = First day of the year (Around 21st -25th March)
Ethuil = Spring
Laer = Summer
Enedhoer = Middle days
Iavas = Harvest
Lasbelin = Leaf-fall, autumn
Firith = Fading
Rhîw = Winter
Echuir = Stirring (early Spring)
Penninor = Last day of the year (Around 20th March)

Mortal reckoning
Narwain = January
Nínui = February
Gwaeron = March
Gwirith = April
Lothron = May
Nórui = June
Cerveth = July
Urui = August
Ivanneth = September
Narbeleth = October
Hithui = November
Girithron = December

They would also of course have used Ethuil, Laer, Iavas/Lasbelin and Rhîw to indicate the four main seasons.

Years

The Elves dealt in both Valian years (where one 'year' is 144 mortal years) and 'sun rounds', which are equivalent to one of our years of 365 days.
Idhrinn or în = Year ('sun round', 365 days)
Ennin = Valian Year 'long year' (144 mortal years)
Andrann = Millennium (a cycle of 144 Valian years)

Further vocabulary