Siman 588
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א זְמַן תְּקִיעַת שׁוֹפָר בַּיּוֹם וְלֹא בַּלַּיְלָה; וּמִצְוָתָהּ מִשְּׁעַת הָנֵץ הַחַמָּה וָאֵילָךְ, וְאִם תָּקַע מִשֶּׁעָלָה עַמּוּד הַשַּׁחַר יָצָא. וְאִם שָׁמַע מִקְצָת תְּקִיעָה קֹדֶם שֶׁעָלָה עַמּוּד הַשַּׁחַר, וּמִקְצָתָהּ אַחַר שֶׁעָלָה עַמּוּד הַשַּׁחַר, לֹא יָצָא. הַגָּה: וְאִם הָיָה שִׁעוּר תְּקִיעָה בְּמַה שֶּׁשָּׁמַע בַּיּוֹם, נִתְבָּאֵר בְּסִימָן תקפ"ז סָעִיף ג'.
1 Time for sounding the shofar, and regarding this there are 5 paragraphs. The time to sound the shofar is during the day, and not at night. The mitzvah is [binding] from the sunrise [netz hachamah, the sun is visible in the horizon] onwards. And if one sounded since dawn [when the sun has began to illuminate but is not yet visible] one has fulfilled the obligation. However, if one heard the shofar being sounded partly before dawn and partly after dawn, one has not fulfilled one's obligation. Rema: And if there was the shiur (minimal halachic amount) of tekiah blasts in that what he heard in the day, see what was explained in Siman 597 Paragraph 3.
ב שָׁמַע ט' תְּקִיעוֹת בְּט' שָׁעוֹת בַּיּוֹם, יָצָא וַאֲפִלּוּ הֵם מִט' בְּנֵי אָדָם תְּקִיעָה מִזֶּה וּתְרוּעָה מִזֶּה וּתְקִיעָה מִזֶּה; וְיֵשׁ אוֹמְרִים דְּדַוְקָא בְּשֶׁלֹּא הִפְסִיק בֵּינֵיהֶם בְּקוֹל שׁוֹפָר שֶׁאֵינוֹ רָאוּי בְּאוֹתָהּ בָּבָא.
2 If one heard 9 teki'ot during 9 hours in the day, one has fulfilled one's obligation. And this is true even if there were 9 different people [blowing], and one heard a teki'ah from one, and a tru'ah from another, and a teki'ah from another, one has fulfilled. And some say specifically when there was not a break between them with a sound of the shofar that was not fit for that set (of blasts).
ג שָׁמַע ט' תְּקִיעוֹת מִט' בְּנֵי אָדָם שֶׁתָּקְעוּ כֻּלָּם כְּאֶחָד, לֹא יָצָא, שֶׁאֵין כָּאן פְּשׁוּטָה לְפָנֶיהָ וּפְשׁוּטָה לְאַחֲרֶיהָ. הַגָּה: וְאִם שְׁנַיִם תָּקְעוּ כְּאֶחָד כָּל הַסֵּדֶר, וַאֲפִלּוּ אֶחָד תָּקַע בַּחֲצוֹצְרוֹת, יָצָא דְּיָהִיב דַּעְתֵּיהּ עַל הַשּׁוֹפָר (הַגָּהוֹת אֲשֵׁרִי וּגְמָרָא פ' רָאוּהוּ בֵּית דִּין).
3 If one hears 9 teki'ot from 9 different people which were sounding the shofar at the same time, one has not fulfilled one's obligation, since there is no simple sound before and after it. Rema: And if two are sounding as one all the order (of blasts), even if one is sounding with a biblical trumpet, one has fulfilled one's obligation as long as one's attention is turned to the shofar.
ד הָיָה זֶה צָרִיךְ פְּשׁוּטָה רִאשׁוֹנָה וְזֶה צָרִיךְ פְּשׁוּטָה אַחֲרוֹנָה, תְּקִיעָה אַחַת מוֹצִיאָה אֶת שְׁנֵיהֶם.
4 This one needed a simple blast at the beginning and this other needed a simple blast at the end, one teki'ah fulfills the obligation of them both.
ה יוֹם טוֹב שֶׁל רֹאשׁ הַשָּׁנָה שֶׁחָל לִהְיוֹת בְּשַׁבָּת אֵין תּוֹקְעִין בְּשׁוֹפָר. הַגָּה: וְאָסוּר לְטַלְטְלוֹ, אִם לֹא לְצֹרֶךְ גּוּפוֹ וּמְקוֹמוֹ (אוֹר זָרוּעַ וְהַגָּהוֹת אֲשֵׁרִי סוֹף פֶּרֶק בַּמֶּה מַּדְלִיקִין).
5 If the holy day of Rosh Hashanah falls on Shabbat we do not sound the shofar. Rema: and it is even forbidden to handle a shofar, unless if needed for itself (i.e. in an allowed Shabbos act like to carry water) or it’s place (i.e. on a chair that one wants to sit).