Today the Shofar is not sounded in preparation for Rosh Hashanah as it was during the month of Elul, to distinguish between the custom and the actual law of sounding the Shofar on Rosh Hashanah.
After the morning prayer, the Annulment of Vows (Hatarat Nedarim) is performed to begin the year free from the burden of things we promised to do but did not. It should be noted that the annulment only applies to promises that the person does not remember making or promises that, had they known they would not be able to keep them, they would not have made. It is customary to recite this before ten men, who act as a court (Beit Din).