Probably the single most consistent debate you can count on seeing in the Celtic Pagan community is about the dating of the four Fire Festivals. Like all such debates each side tends to hold its own view quite passionately. There are three main arguments: the dates of the celebrations were set astronomically; the dates were set using a calendar; the dates were based on agricultural signs. Each side has merit, but the truth is there is not enough solid evidence to ever know with certainty how the ancients timed their celebrations.
The astrology argument is based on setting the dates exactly midway between the solstices and equinoxes. This usually puts them roughly six weeks after the previous holiday and six weeks before the next one. In some cases people suggest using a specific marker such as a constellation being at a certain point in the sky or a sign of the zodiac at a certain degree. The ancient stone circles and mounds which are aligned with certain times are also used, so that when the light of the sun hits a certain point or illuminates the interior of the mound it would indicate that the holiday should be celebrated. This argument naturally hinges on two premises: that the ancients celebrated the solar holidays as well, and that they were aware of the alignments of the ancient neolithic monuments. There is also a related argument that uses lunar dating, based from what I have seen on the second full moon after the solar event*.
The calendar argument dates the celebration on the first day of the respective months they occur on: February, May, August, and November. We have references in the mythology dating back to the 11th century of Lughnasa, Bealtaine, and Samhain being on the 'kalends' (first day) of those months and we know historically they were celebrated on those days in folk practice. This is somewhat complicated by the fact that the calendar system switched from the Julian to the Gregorian and when that occurred the dates shifted. When the calendar shift occurred in the UK in 1752 it moved everything back 11 days, meaning what was the first of November is now the 12th. Even a hundred years ago in several areas people were still celebrating Imbolc and Lughnasa in particular on the 12th of February and August respectively because they were using the old dating. What this means in practice is that when we see older references to the days being celebrated on the first we need to understand that they are equivalent for us today to the 12th of that same month. A Celtic Reconstructionist who wanted to use the calendar dates could, I think, choose to either go by the first of the month still or use the older dating and celebrate on the 12th.
The final method of dating the celebration of the holiday is based on observation of agricultural markers and the idea that each holiday is agrarian at heart and depends on certain conditions being met. Imbolc is a celebration of the return of fresh milk and would be celebrated when the lambs were born or the sheep came into milk. Bealtaine is the beginning of summer, a time when the herds are moved to summer pastures, and would have been celebrated when the people were confident winter had passed; this is often said to be marked by the blooming of the Hawthorn and indeed many Bealtaine traditions require flowers. Lughnasa was the beginning of the harvest - nothing could be harvested before the proper time by longstanding tradition - and of the harvest fairs, and would have been celebrated when the grain crops were ready to be gathered. Samhain was the beginning of winter, when the herds were brought back in from the summer pastures and extra stock was butchered. It also marked the end of the harvest and gathering anything after Samhain was prohibited as everything left belonged to the daoine sidhe. Many people say that Samhain would have been celebrated after the first hard frost; there is a certain logic to this as frost would ruin any crops left in the fields**. This method of dating is the least rigid and most changeable of the three, and also can prove difficult for people who are far removed from the farming cycle.
Each of these approaches has merit, and each has problems. No one is a perfect solution or can be proven beyond question to be the historical method. It is up to individuals to decide which method they prefer and learn how best to apply it within their own practice.
*there may well be variations of this
**different crops have various tolerances to frost, and this is somewhat dependent on the severity and length of the frost as well, however it seems safe to say that our ancestors would be highly motivated to get all the crops in by the time they started seeing frost and would consider frost a sign of the end of the harvest season and beginning of winter.