Tekufot are the Halachic equivalents of the yearly solar seasons, which we have four of yearly; Nissan/Spring, Tamuz/Summer, Tishri/Fall & Tevet/Winter. There are two practical concepts that depend on when the beginning of each Tekufa falls out (רש”י על שמות ל”ד:כ”ב - “שֶׁהִיא בַחֲזָרַת - בִּתְחִלַּת”):

• Outside ארץ ישראל, we switch the text of תפילת שמונה עשרי from ברכנו to ברך עלינו after 60 days into Tekufat Tishri (ש”ע או”ח קי”ז:י”א). Although this currently corresponds to December 4^th (or December 5^th), this will drift outside of those days as the years go.
• There is a custom that developed not to drink plain water at the beginning of the Tekufah itself (רמ”א על יורה דעה קט”ז:ה). Beyond those who follow this for the simple reason of starting off the Tekufah with something important (תשובות הגאונים (מוסאפיה) סי’ י”ד), the concept is stressed in a stronger fashion among Kabbalistic circles, warning of the spiritual danger that befalls during this time (פרי חדש על ש”ע או”ח סוף סימן תכ”ח מזהיר על חשש המוות). As such, some took an additional “time-buffer” before and after the time. Although they range from 15 minutes (חיד”א, שו”ת יוסף אומץ סימן מ”ב) to 3 hours (מנהגי מהרי”ל בליקוטים של סימן נו), the common minhagim have been to wait either an hour and a half prior and following (Rabbi Mazuz on Djerban Minhagim; רמ”ך בברית כהונה - חלק אורח חיים מערכת ת’ אותיות כ”א-כ”ה), or half an hour prior and following (נהר מצרים, דף עז ע”ב; ר’ אלינו חזון בספר נוה שלום סימן קט”ז אות ה). Maran zt”l concludes like the latter of the two, as recorded in Halichot Olam (vol. VII, pg. 183).

To know which date a תקופה will fall out on, one must have a point of reference when a known תקופה was. The easiest known תקופה is the one recorded in משנה תורה, הלכות קידוש החדש (9:4), due to it being the first תקופה of the world. From there, you’ll need to add the length of a season, which is as simple as taking the length of a year divided by four.

• We hold like שמואל (Bavli Eruvin, 56a) that a year is 365.25 days. Thereby, dividing that into four gives us the season’s length of 91 days, 7 hours and 30 minutes. This rounded value of 365.25 is used for the sake of being easier to keep track of (Hazon Ish - OC Siman 138, se’if katan 4).
• A further debate is whether these Tekufot used a fixed clock time of 12:00 PM or used local Israel Hatzot. Although the Ohr Hachaim calendar uses the fixed clock time like Rav Tuchanski does in his calendar, the תנובות שדה (Rav Aharon Boron) takes issue with this due to the arbitrary nature of a 12:00 midpoint. As such, the עמודי הוראה calendar (as well with the unofficial לוח ילקוט יוסף) uses the local Israel Hatzot time of 11:39 AM, which is only a -21 minute difference. For the water warning above, it is possible to accomodate both by starting the time period with R Boron’s time and finishing by the time listed in the Ohr Hachaim calendar.