When Yom Kippur falls on Shabbos, the entire congregation repeats וַיְכֻלּוּ, in testimony of our belief that God created Heaven and earth. According to the Halacha, when one is a witness, he must stand and declare his testimony aloud.
וַיְכֻלּוּ הַשָּׁמַֽיִם וְהָאָֽרֶץ וְכָל־צְבָאָם: וַיְכַל אֱלֹהִים בַּיּוֹם הַשְּׁבִיעִי מְלַאכְתּוֹ אֲשֶׁר עָשָׂה. וַיִּשְׁבֹּת בַּיּוֹם הַשְּׁבִיעִי מִכָּל־מְלַאכְתּוֹ אֲשֶׁר עָשָׂה: וַיְבָֽרֶךְ אֱלֹהִים אֶת־יוֹם הַשְּׁבִיעִי וַיְקַדֵּשׁ אֹתוֹ. כִּי בוֹ שָׁבַת מִכָּל־מְלַאכְתּוֹ אֲשֶׁר־בָּרָא אֱלֹהִים לַעֲשׂוֹת: The heavens and the earth were completed and [so were] all their hosts. And God completed by the seventh day His work which He had done, and He abstained on the seventh day, from all His work which He had done. And God blessed the seventh day and sanctified it for on it He abstained from all His work which God had created to do.
The following prayer, בְּרָכָה מֵעֵין שֶׁבַע the abridged form of the seven blessings of the Maariv Amidah, is said only by the Chazzan.
חזן: בָּרוּךְ אַתָּה יְהֹוָה אֱלֹהֵֽינוּ וֵאלֹהֵי אֲבוֹתֵֽינוּ אֱלֹהֵי אַבְרָהָם אֱלֹהֵי יִצְחָק וֵאלֹהֵי יַעֲקֹב הָאֵל הַגָּדוֹל הַגִּבּוֹר וְהַנּוֹרָא. אֵל עֶלְיוֹן קוֹנֵה שָׁמַֽיִם וָאָֽרֶץ: Blessed are You, Adonoy, our God and God of our fathers, God of Avraham, God of Yitzchak, and God of Yaakov; the Almighty, the Great, the Powerful, the Awesome, the most high Almighty, Possessor of heaven and earth.
The congregation may recite the following paragraph, which should then be repeated aloud and in its entirety by the Chazzan.
מָגֵן אָבוֹת בִּדְבָרוֹ. מְחַיֵּה מֵתִים בְּמַאֲמָרוֹ. הַמֶּלֶךְ הַקָּדוֹשׁ שֶׁאֵין כָּמֽוֹהוּ. הַמֵּנִֽיחַ לְעַמּוֹ בְּיוֹם שַׁבַּת קָדְשׁוֹ. כִּי בָם רָצָה לְהָנִֽיחַ לָהֶם. לְפָנָיו נַעֲבוֹד בְּיִרְאָה וָפַֽחַד. וְנוֹדֶה לִשְׁמוֹ בְּכָל יוֹם תָּמִיד מֵעֵין הַבְּרָכוֹת: אֵל הַהוֹדָאוֹת. אֲדוֹן הַשָּׁלוֹם. מְקַדֵּשׁ הַשַּׁבָּת וּמְבָרֵךְ שְׁבִיעִי. וּמֵנִֽיחַ בִּקְדֻשָּׁה לְעַם מְדֻשְּׁנֵי עֹֽנֶג זֵֽכֶר לְמַעֲשֵׂה בְרֵאשִׁית: Shield of [our] fathers with His word, Resurrector of the dead with His utterance; the King, the Holy One Who has no peer. He gives rest to His people on the day of His holy Shabbos for with them He was pleased to grant them rest. Before Him we will serve with fear and trepidation, and give thanks to His Name every day continuously, from the essence of the blessings. Almighty of thanksgiving, Master of peace, Sanctifier of the Shabbos, Who blesses the seventh day and grants rest in sanctity to a people sated with delight— in commemoration of the work of creation.
אֱלֹהֵֽינוּ וֵאלֹהֵי אֲבוֹתֵֽינוּ רְצֵה נָא בִמְנוּחָתֵֽנוּ. קַדְּשֵֽׁנוּ בְּמִצְוֹתֶֽיךָ וְתֵן חֶלְקֵֽנוּ בְּתוֹרָתֶֽךָ שַׂבְּעֵֽנוּ מִטּוּבֶֽךָ. וְשַׂמְּחֵֽנוּ בִּישׁוּעָתֶֽךָ: וְטַהֵר לִבֵּֽנוּ לְעָבְדְּךָ בֶּאֱמֶת. וְהַנְחִילֵֽנוּ יְהֹוָה אֱלֹהֵֽינוּ בְּאַהֲבָה וּבְרָצוֹן שַׁבַּת קָדְשֶֽׁךָ. וְיָנֽוּחוּ בָהּ יִשְׂרָאֵל מְקַדְּשֵׁי שְׁמֶֽךָ. בָּרוּךְ אַתָּה יְהֹוָה מְקַדֵּשׁ הַשַּׁבָּת: Our God, and God of our fathers, be pleased with our rest, sanctify us with Your commandments and give us our share in Your Torah; satisfy us from Your goodness and gladden us with Your deliverance, and purify our hearts to serve You in truth. And give us as our inheritance, Adonoy our God, in love and in pleasure Your holy Shabbos; and may Yisrael rest thereon— the sanctifiers of Your Name. Blessed are You Adonoy, Sanctifier of Shabbos.