A little halacha from the Mishna Berurah l’kavod the C”C’s yahrtzeit:
The Rama (585:3) writes that it is best (“tov”) to blow shofar from the right side of the mouth.
The Mishna Berurah quotes two explanations from the Magen Avraham for the minhag: 1) to counter the influence of the satan who stands to the right, as the pasuk says, “v’hasatan omeid al y’mino l’sitno”; 2) the left is already protected by the tefillin worn on the left hand (quoted in the Sha’ar haTziyun). The Biur Halacha adds another explanation which the C”C heard in the name of R’ Meir Simcha (I am far from a baki in M”B, but for what it's worth, I don’t recall other quotations from RMS in the MB): the gemara derives tekiya from the blowing of chatzotzros in battle; in the description of the battle fought by Gidon in Nach we learn that the chatzotzros were held in the soldiers’ right hand and torches in the left.
Since my son is a lefty I am somewhat more attuned to halachos that emphasize right-handedness and have come to expect debate as to whether things are reversed for leftys. This is no exception. Whether a lefty should blow out of the left side of his mouth should at first glance depend on which reason above is paramount: according to reason #1 and the reason given by RMS, both a righty and a lefty should blow out of the right side of the mouth. However, according to reason #2, a lefty who wears tefillin on his right arm should blow shofar out of the left side of his mouth because the “protections” would be reversed.
The M”B in the Sha’ar haTziyun rejects this nafka minah (and therefore he tucks reason #2 in the Sha’ar haTziyun where most people won’t see it and get confused). When we speak of the protective power of tefillin, we are not speaking viz a viz the particular ba’al toke’a, but viz a viz ba’alei tekiya in general. Since the majority of people are righthanded and wear tefillin on their left arm, the shofar is blown from the right by all.
(R' Menashe haKatan in Mishaneh Halachos Mh”T O.C. #480 was asked halacha l’ma’aseh how a lefty ba’al toke’a should hold the shofar. He replied by quoting this M.B. B’dieved, one is yotzei either way.)