Tekufot are displayed according to the opinion of Shmuel (Eruvin 56a, Mishneh Torah 9:4). Shmuel's opinion is used for most halachic purposes today.
The schedule of weekly Torah readings is governed by the rules set out in Tur, Orach Chaim 428. There are 14 year types, determined by: (1) the day of the week of Rosh Hashana, (2) whether Cheshvan and Kislev have their standard number of days, and (3) the day of the week of the first day of Pesach. Printed halakhic works include tables of these types (e.g., this table). The rules for merging and splitting certain parsha pairs were codified by R. Chaim Mordechai haCohen Brecher (see table).
Each year type is encoded with three Hebrew letters: the day of Rosh Hashana (ב Mon · ג Tue · ה Thu · ז Sat), the year length (ח deficient · כ regular · ש complete), and the day of Pesach. This code appears in Chumashim and Tikun Korim (e.g., here). The year type also uniquely determines whether the year is a leap year.
In some years certain readings in Eretz Israel may differ from the Diaspora because a second day of Yom Tov displaces a reading in the Diaspora. For this reason the table below shows both readings depending on location.
Look up the public Torah reading with its haftarah on a given day — Shabbat, a festival, or a fast — according to your minhag.
This page is for convenience to look up dates documented in the Julian calendar. Various countries adopted the Gregorian calendar at different times — e.g. Russia in 1918, Greece in 1923. You can look up the adoption dates by country here.