The Hebcal Torah Readings page lists all of the 54 parashiyot. Each individual parashah page includes an aliyah-by-aliyah breakdown of what sections are read.
See also Judaism 101: Torah Readings.
Jews living in the Diaspora (outside of modern Israel) typically observe two days of chag on holidays that are Yom Tov (holidays where work is forbidden, called yontiff in Yiddish). In Israel, only one day of chag is observed.
Sometimes, depending on the calendar, the Diaspora observes the second day of chag on Shabbat, and the holiday Torah reading pushes the regular weekly Torah reading back a week. Since Israel has only one day of chag, they read the regular weekly Torah reading. Thus, the Parashat ha-Shavuah ends up being different.
When using the “Weekly Torah portion on Saturdays” option on the custom calendar, select the appropriate option depending on where you live (Israeli holiday schedule for those living inside Israel, Diaspora for everyone else).
“Many congregations pattern their weekly Torah reading cycle after a system similar to the one used in ancient Israel during the rabbinic period. In this system, the traditional parashiot are each divided into three shorter segments, and the whole Torah is completed once every three years. The system has both advantages and disadvantages, but its ability to shorten the length of Torah reading without sacrificing the complete reading of the Torah on a regular basis has made it the choice of some synagogues in the Conservative Movement.”
A Complete Triennial System for Reading the Torah, Committee on Jewish Law and Standards of the Rabbinical Assembly
Leyning coordinators can download these Comma Separated Value (CSV) files and import into Microsoft Excel or some other spreadsheet program. These spreadsheets contain the Torah readings for the current year and 5+ years into the future.
Note that in September 2013, we replaced the large multi-year fullkriyah.csv file with separate files for each Hebrew year.