I have done this several times in the past. In viewing the Mishnah Brurah, now, I discovered several things that I was unaware of. As there are many laws regarding blowing / hearing the shofar, what I am providing may be a partial list, only:
- 589:3 - a woman is exempt from hearing the shofar b/c it is a time bound mitzvah. The mechaber states that they should not make a bracha and others should not make one for them.
- Magen Avraham (see Mishnah Brurah par. 11) states that one should not blow during the 1st 3 hours of the day. There are other caveats mentioned there, as well, that I couldn't quite decipher (sorry.)
- Regarding standing, the only item I noticed was something about the person blowing the shofar should stand. As for the congregation, in actuality, the shofar blowing that precedes Musaph is called "teki'ot dimeyushav" - "blasts of SITTING" to contrast this with "Tki'ot d'meumad" - blasts of standing which refers to the blasts done during Shmoneh Esreh (b/c people stand for Shmoneh Esreh.) Sefardim do teki'ot during the silent Amidah as well as the chazan's repition, but in both forms, people should stand, there. Apparently, standing for the blasts prior to Musaph, has become an accepted minhag - I have to locate the source for that; don't recall, offhand, where I saw this.
- An individual at home should not have the blasts done in the middle of his Shemonah Esreh, but rather should wait to hear them after he is finsished. Also, he cannot hear shofar blasts until after he has said Shemoneh Esreh - see 592:2 and 594:1.
- From my understanding of 585:5, the use of a "makri" - someone who announces the order of the blasts is primarily for the Shat"z, so that he does not become confused. However, the commentaries, there, state, that if he is confident that he would not become confused, he does not need a "makri". I am devising a "kal vachomer" that if this is said about the Shat"z, who is performing 2 tasks, and there is a leniency for him, than someone who is NOT a Shat"z does not require a "makri" either in shul or when blowing privately, if he will not be confused.
In shul, I have had a "mix". (I am not the shat"z for Musaph, BTW). The makri has been present at the beginning of the blowing (the first 30), but since we have 2 concurrent minyanim, he tends to disappear and be the makri at the other minyan. (Don't ask me why he never returned to us, later. Personally, I think he went home, as the other minyan finished long before us.) I did the remaining blasts without a makri, and I was not confused (other than why the makri didn't reappear :-) At the person's home, there was no makri.
Other than these, I didn't notice any significant differences between what happens in home vs. in shul. Again, I may have missed something buried in the commentaries, so check them, again.
When I have done shofar blowing in someone's home, it has usually been after shul is finished and after I have blown shofar in shul. I am quite exhausted, so I have taken the leniency to sound 30 blasts, and if I'm really tired or the person I'm blowing for is too frail or impatient (True story - one year, a woman died 3 hours after I had left her home from blowing shofar for her. When the rav in my shul heard this story, he jokingly said that my shofar blowing killed her! Weird incident... can't make this up!) I blow just 10 blasts to fulfill the Torah commandment.