“In the seventh month.” At this time in Israel’s history, the seventh month was the month Tishri. Before the Exodus, the seventh month was Abib (also called “Nisan”), but God changed Abib to the first month of the year (Exod. 12:1-2).
“on the first day of the month.” The first day of the month was the new moon, and there were special sacrifices and offerings done on every new moon that dedicated the new month to God (Num. 28:11-15; 10:10). But on the seventh month there were additional sacrifices and offerings.
“shofar.” The ram’s horn trumpet, not the metal trumpet.