The various calendars in use at the time of The Lord of the Rings are similar to ours. Like ours, they are based on the movements of the Sun and Moon.
In Valinor, before the creation of the Sun and Moon, time was measured by the waxing and waning of the lights of the Two Trees. I won't go into details as the question only asked about calendars in Middle-earth, but the measuring of time in Valinor is described in The Silmarillion (Chapter 1 of Quenta Silmarillion) and in Morgoth's Ring (The Annals of Aman).
Tolkien describes some of the calendars of Middle-earth in Appendix D of The Lord of the Rings.
He starts out describing the length of a year:
The year no doubt was of the same length1, for long ago as those times are now reckoned in years and lives of men, they were not very remote according to the memory of the Earth.
1365 days, 5 hours, 48 minutes, 46 seconds.
The Lord of the Rings Appendix D: Calendars
Page 1107 (Single volume 50th Anniversary Edition)
Here are some notes on the various calendars. To avoid making this an extremely long post, I won't quote all the source material, but if you are interested you should read Appendix D.
Numbering of years
All the calendars include years of about the same length, although different peoples may start the year at different times. Most of peoples of the west (except hobbits of The Shire) share the same way of numbering year.
- The First Age began with the first rising of the Sun.
- The Second Age began with the defeat of Morgoth and the founding of Númenor.
- The Third Age began with the death of Sauron by the Last Alliance.
- The Fourth Age began with the departure of the ring-bearers from Middle Earth
With each new Age, the count of years began again at "1".
In The Shire, hobbits counted the years from the founding of the Shire (in Third Age 1601). They call this "Shire Reckoning".
The Eldar in Middle-earth
The Eldar (being immortal) used very long measures of time. A yén consisted of 144 solar years, and was divided into 8,766 enquier (similar to a week but with only 6 days). As they were interested in the seasonal changes in vegetation, they also tracked the solar year which they called a loa.
The Eldar preferred to reckon in sixes and twelves as far as possible.
The Lord of the Rings Appendix D: Calendars
Page 1107 (Single volume 50th Anniversary Edition)
In the calendar of Rivendell, the loa began in spring and was divided into six seasons (two had 72 days and the rest had 54). That made 360 solar days (the elves liked to count in sixes). To match the solar year, they added five additional days (one at the start of the year, three in the middle and one at the end). Instead of leap years, they doubled the three extra days in the middle of the year every 12 years).
King's Reckoning
This was the calendar used in Númenor, and in Arnor and Gondor until the end of the kings. It had weeks of 7 days. The year began in midwinter and consisted of 12 months. The 6th and 7th months had 31 days and the rest had 30. There were three additional days (not part of any month) at the start, middle and end of the year. Every fourth year (except a century year), there were two middle days instead of one. There were also adjustments made every millennium to more closely match the solar year.
Kings Reckoning began with the founding on Númenor at the beginning of the Second Age.
Steward's Reckoning
This was introduced by Mardil the Steward in part to correct inaccuracies in the millennial adjustments that were introduced when the Third Age began in the middle of a millennium.
In this calendar, the 6th and 7th months were reduced to 30 days (like the rest), and the two extra days were moved to between the 3rd and 4th months and between the 9th and 10th month.
Shire Reckoning
The Shire Calendar is reproduced at the start of Appendix D. The year is split into 12 months, each with 30 numbered days. In order to pad the year out to match a solar year, some months have additional days with names but no number:
- The first day of the first month (called Yule)
- The last day of the 12th month (also called Yule)
- The last day of the 6th month (called Lithe)
- The first day of the 7th month (also called Lithe)
That makes 364 days and exactly 52 weeks (of 7 days each). Between the two days is an additional day called Midyear's Day that was not considered part of any week (it was an extra day between Friday and Saturday). In leap years, another day called Overlithe (also not part of any week) was added after Midyear's Day to keep the calendar approximately in synch with the solar year.