The Shire Reckoning
As stated in the appendices of LotR, the Shire Reckoning is a slightly modified form of the King's Reckoning of old Arnor, which was brought from Numenor. Now, to connect the Eldarin to the Shire calendar: The general correspondence is: Yestare = Astron 6; Ethuil = Astron 7 - Thrimidge 30; Laer = Forelithe 1 - Wedmath 9; Iavas = Wedmath 10 - Winterfilth 3; the Enderi = Winterfilth 4 - 6; Firith = Winterfilth 7 - Blotmath 30; Rhiw = Foreyule 1 - Solmath 10; Echuir = Solmath 11 - Astron 4; Mettare Astr on 5. Supposedly the Elves began their reckoning immediately from the rising of the Sun, 590 years before the end of the First Age. (Another era that might be remembered would be _o thangadad Imladris_, from the founding of Imladris in SA 1697.)
So, for example, TA 3008 is the 7039th from the rising of the Sun, and the 7th year of the 11th cycle (3002-3013) of the 49th yen (2882-3025) since then. Since Astron 6 of 3019 and 3020 are stated to have been _yestari_, I have been able to calibrate the Shire Reckoning and the Imladris calendar: within the present cycle, Yestare of TA 3002, 3003, and 3004 fell on Astron 7; in TA 3005, 3006, 3007, 3008 it falls on Astron 6; in TA 3009, 3010, 3011, 3012 it will fall on Astron 5; in TA 3013 it will fall on Astron 4, but that year will contain 6 _enderi_ and in TA 3014 it will fall on Astron 7. Since the Shire Leap-day (Overlithe), occurring in TA 3004, 3008, 3012, was in midsummer, after yestare, the date of yestare changes on the _following_ year.
Steward's Reckoning
The Stewards' Reckoning and the Shire Reckoning are very close, almost identical except for their treatment of the intermediate days; this throws the six middle months of the year off by one day, but returns it to synch by the end of the year. (The Steward's Reckoning is also a slight revision of the King's Reckoning.) Since their treatment of leap years and so on is exactly the same, relating the two recko nings is only a question of figuring out what date corresponds to what date. There is no good way to figure out what the day-names for particular dates in Stewards' Reckoning were, because we don't have a single example.
It is stated in the appendices of LotR that Dunedain of Arnor used the Sindarin names of the months. Both the Arnorian and Gondorian Dunedain, though, would probably have used the Quenya names, with pronunciation slightly altered, when speaking Westron; and would also have used the Quenya names when speaking or writing Quenya; but would have used the Sindarin names when speaking Sindarin, just as a medieval or Renaissance Englishman would use _January_, _February_ in speaking English, _Ianuarius_, _Februarius_ in speaking or writing Latin, but _Janvier_, _Fevrier_ in speaking or writing French, his English usage being thus closer to the Latin than his French.
Ingenediad Imladris (Rivendell Year-reckoning)
A clue to the era by which the Elves of Imladris calculated their calendar (which is not necessarily the same as the era they would have used in dating) is given in Appendix D to LotR: "That there was an inaccuracy (in the length of a twelve-year calendar cycle) is shown by a note in the Calendars of the Red Book to the effect that in the 'Reckoning of Rivendell' the last year of every third yen was shortened by three days; the doubling of the three enderi due in that year was omitted; 'but that has not happened in our time'." What does 'in our time' mean? Probably it refers to the 'time' of the Hobbits who compiled information into the additions to the Red Book of Westmarch after the War of the Ring, that is, in their experience or lifetime. This would probably correspond the the lifetimes of Peregrin, Meriadoc, and Samwise, the last decade or two of the Third Age, and the first seventy years or so of the Fourth.
Looking at different possible eras, and calculating the different times at which the end of a third yen (a 432-year period) could have fallen, we find that the 45th yen and 15th three-yen period from the Fall of Morgoth and beginning of the Second Age ended in Third Age 3039 (Fourth Age 19); the 33rd yen and 11th three-yen period from the Founding of Imladris ended in Third Age 3008; and the 21st yen and 7th three-yen period from the beginning of the Third Age ended in Third Age 3024 (Fourth Age 4). All of these can be reasonably interpreted as 'in our time'. The only era so far suggested which does not have a three-yen period ending 'in our time' is an era counted from the Rising of the Sun; of which the 48th yen ended in Third Age 2881, and the 51st yen ended in Third Age 3313 = Fourth Age 293, neither date of which can be plausibly considered 'in our time'. So, it seems most likely that this particular calculation proceeded from the date of the Rising of the Sun.