Growing up we celebrated Rosh Hashanah basically the same way every year. First off, all Jewish holidays start the sundown before. So that night we would have a nice dinner...usually chicken, veggies, soup and challah (a type of bread). But the next day (the holiday is 2 days) we would go to Synagogue and pray and then pray some more as well as hear the shofar. After services, we would noramlly go to a friends house for a late lunch and spend time with friends.
Another thing we believe is that from the start of Rosh Hashanah and to the end of Yom Kippur we believe if we do good we will be written into the Book of Life.