The shofar or ram's horn has been used to call Jews together at least since the Exodus from Egypt (Yetziat Mizrayim). Today it is played in the synagogue on weekdays after morning services (Shacharit) throughout the month of Elul, culminating on Rosh haShanah (New Year) and Yom Kippur (Day of Atonement) in the month of Tishrei. In the Jewish tradition, this represents the forty days Moses spent on Mount Sinai betreen the incident of the Golden Calf (Egel haZahav) and the gift of the second set of tablets (Sh'nei Luchot haBrit) containing the Ten Commandments (Aseret haDibrot).
There are four "notes" played in various patterns throughout the High Holiday services. T'ki'ah ia a long, uninterrupted blast. Sh'varim (broken) is three short blasts. T'ruah is approximately nine very short toots. T'ki'ah g'dolah is basically a T'ki'ah held for as long as one has breath.
Playing a shofar requires practice. It is very similar to playing a trumpet, or any brass instrument, except that the mouthpiece is not as easy to use. Basically, one presses one's lips together and forces breath out through them, producing the sort of vibration we all remember from kindergarten. Holding the shofar against one's vibrating lips produces the clarion, inchoate call we all know so well.
But here's the catch: Each shofar is unique, and most are not deliberately worked into a nice, symmetrical, trumpet-like mouth piece. The only way to get one to work is to hold it up to one's mouth and try and try and TRY……. until that sound starts coming out.
B'hatzlachah! (Best of luck!)