The Jewish calendar has different months and a different reckoning of time from the Roman (some people call it Christian) calendar. The first month of the Jewish calendar is Nisan, which usually corresponds to March/April. However, the New Year that is more widely celebrated is actually the first of the seventh month, known as Tishrei. Tishrei usually corresponds to September/October, and the first day of this month is called Rosh Hashanah (the head of the year).
It is customary for Jewish people to greet one another by saying, La shanah tova tikatevu" (may your name be inscribed for a good year). A traditional blessing said at this time is known as the Shehechianu: "Blessed art Thou O Lord our God, King of the Universe who has kept us and sustained us and brought us to this season."
Another tradition at Rosh Hashanah is eating fruits and honey cake to symbolize the hopefulness for the year ahead. We also eat apples dipped in honey. The tradition of eating sweet foods is based on a biblical event from the time of Ezra. The people of Israel celebrated the first of the seventh month by reading the Scriptures together in Jerusalem. At the conclusion of the reading, the people were instructed, "Go your way, eat of the fat, drink the sweet, and send portions to those for whom nothing is prepared; for this day is holy to our Lord. Do not sorrow, for the joy of the Lord is your strength" (Nehemiah 8:10). God is pleased with new beginnings, and He wants us to celebrate and enjoy His goodness, past, present and future.
It is customary to send New Year's greeting cards at this season, wishing friends and family health and strength for the coming year. People generally send such cards from a week ahead of Rosh Hashanah until a week or so after. If it is not too late, you might want to pick up a few New Year's greeting cards to send to your Jewish friends. They will appreciate your thinking of them during this special time of year, just as you appreciate their thoughtfulness in sending you Christmas greetings.