The term Celtic calendar is used to refer to a variety of calendars used by Celtic-speaking peoples at different times in history.
A neolithic engraved stone found at Knowth, Ireland, may be a graphical representation of a lunar calendar. While pre-dating the insular "Celts" by over 2500(?) years, Brennan (1994) speculates that it operates on the same principle as the Coligny calendar.
Continental Celtic Calendar
Possibly the oldest material Celtic calendar is the fragmented Coligny calendar, which was discovered in Coligny, France, in 1897. It uses Roman numerals and dates to the 1st century BCE, a time when the Roman Empire imposed use of the Julian Calendar in Roman Gaul.
The Coligny calendar was lunisolar- a way to reconcile lunations and the solar year. The astronomical format of the calendar year that the Coligny calendar represents, may well be far older, as calendars are usually even more conservative than rites and cults. The date of its inception is unknown, but correspondences of Insular Celtic and Continental Celtic calendars suggest that some early form may date to Proto-Celtic times, roughly 800 BC.
The Coligny calendar registers a five-year cycle of 62 lunar months, divided in a "bright" and a "dark" half-moon or fortnight each. The months were taken to begin at full moon, and a 13th intercalary month was added every two and a half years to align the lunations with the solar year.
Mediaeval Irish and Welsh Calendars
The light half of the year ended at Samhain, which was the first of November, never far from what would become Halloween and the following All Saints Day in our modern calendar. The second part of the year started at Beltaine which was around the first of May.
Celtic days began at night: "they keep birthdays and the beginnings of months and years in such an order that the day follows the night," per their adversary Julius Caesar in his Gallic Wars. Although Caesar says "at night" he specifically does not say "sunset" so we do not know how much the Gauls' differed from our own method of counting from midnights. Longer periods were reckoned in nights, as in the surviving term "fortnight."
"Celtic New Year" Factoid
The popular literature over the last century or so has given birth to the near universal assumption that Samhain, now associated with the Roman Catholic theme and folkways of Hallowe'en, was the "Celtic New Year". A number of sources including both the work of scholarly historians and Neopagan writers have begun to place this assertion under the microscope. In his exhaustive study of the folk calendar of the British Isles "Stations of the Sun"(Oxford University Press, 1996), the historian Ronald Hutton points out that there are no references earlier than the 18th century in either church or civic records which attest to this usage. Although it may be generally correct to refer to Samhain as "Summer's End", this point of descent into the year's darkness may need better proof for us to cite this "end" as also being a "beginning". On the other hand, there -is- a huge volume of proof of the western world, including late Celtia, as having begun their calendars either at the end of December, or around March 25th, at various periods back through and before Medieval times.
In some Neopagan religions, a Celtic calendar based on that of Mediaeval Ireland is observed for purposes of ritual. This does not necessarily indicate that a Celtic language is used for ritual. In other cases, the four Irish festivals of Samhain, Imbolc, Beltane and Lughnassadh are combined with the solstices and equinoxes to produce the modern Neopagan Wheel of the Year. Syncretistic Neopagans are sometimes also influenced by Robert Graves' "Celtic Astrology", which has no foundation in historical calendars.