The basic way to blow the shofar is actually an argument. The Tekia is one long blast. the sevarim is three shorter ones that would fill up the tekia. The truah is 18 short ones that each set of three would fill up one of the three sevarim. But some say 9 short ones.(The Gemara itself is on the last two pages of Rosh Hashana and brought own by Rav Joseph Karo.)

Also the way to do the shevarim is the starting low and going high as brought in הגהות מיימוניות

It is rare to hear anyone doing this right. The best idea is to get your own shofar.