Shulchan Aruch Chapter 588: The Time for Blowing the Shofer (5 Paragraphs)
Note: The REMA / RAMA is in brackets 
1. The time for blowing the Shofer is during the day and not during the night. The Mitzvah is after sunrise. But if you blew the Shofer at daybreak (עמוד השׁחר), you fulfill the commandment. If you hear part of the blowing of the Shofer before daybreak and part after daybreak, you do not fulfill the commandment. [However, if you heard enough after daybreak to fulfill the requirement, it is discussed in 587:3]
2. If you heard nine blows at nine different times during the day, you fulfill the commandment, even if you heard from nine different people a Tekiah from one, a Teruah from another and a Tekiah from another. Some say, that this only applies if there was no interruption between these Shofer blasts. (For if there was an interruption) you would be unable to put them together (lit. “for it is not proper in that section/group”).
3. If you heard nine blows from nine people acting together as one, you do not fulfill the commandment, since in this situation, there is nothing of substance before and after (each blow). [If two people blew the Shofer together, even if they have different sounds , they fulfill the commandment since he (the listener) paid close attention to the Shofer.]
5. If Rosh Hashanah falls out on Shabbat, we do not blow the Shofer. [It is forbidden to move it unless you need the place it is sitting on for a different item (לצורך גופו ומקומו) ].
Translated by Jay Dinovitser www.ShulchanArach.com 6/25/2006
 The Mishna Brura writes that in this case, all nine blow the Shofer at the same time. One blows a Tekiah, the next one blows the Teruah and the third one blows the next Tekiah and so on all at the same time.
 פשׂוטה literally means “simple”. Taking the context and the Mishna Brura into consideration, it means “something” or “substance”; ie: “there is nothing of substance...”.
 Lit. “And if two blew like one the whole order ...” This phrase is translated according to the M.B.
 I did not know what the original phrase “even if one blew with the trumpet (בחצוצרות)” refers too. The Mishna Brura translated it as I wrote above “even though they have different sounds”. He probably translates בחצוצרות as a trumpet like sound. “Even though one sounds like a trumpet...”
 M.B: Even though everyone agrees that normally two simultaneous sounds can’t be distinguished, here is different since the listener loves the Mitzvah so he is sure to pay extra attention. In the case where three blow the Shofer togeather, there is an argument whether you fulfill the commandment of hearing the Shofer.
 This is referring back to the case of nine people blowing the Shofer as one. See the first footnote.
 If one blew a Tekiah, one blew a Shevarim and the next one blew a Tekiah, then the Shofer blows are in sequence and you fulfill the commandment like paragraph 2 where nine people blew the Shofer in sequence.
 Biblically, it is a commandment to blow the Shofer, even on Shabbat. However, the Rabbis were afraid that someone would mistakenly carry the Shofer on Shabbat to temple (which would violate a Biblical negative commandment to not carry on Shabbat) so they instituted a Rabbinical ordinance not to blow the Shofer. According to the Oral Law passed down through Moses, the Rabbis have the authority to construct fences around the Torah to protect its observance so the ancient Rabbis instituted several decrees. The Rabbis also decreed that the four species can’t be used on Shabbat for the same reason. The Rabbis were extremely brilliant with this decree, since one of my friends told me that he accidentally carried the four species to temple on Shabbat when he just became religious. Luckily for him, there was an Eruv. However, if there was no Eruv, he would have transgressed a big sin. If he accidentally carried with the decree, imagine how many Jews would have made a similar mistake without the decree.
You can’t touch the Shofer on Shabbat since there is a rule that a vessel that has a forbidden use can’t be touched.