Birkat Hagomel is the blessing a person recites upon emerging safely from a situation of danger. The birthing process is included among these situations of danger, and tradition directs the woman who is alive and well after giving birth to recite this blessing. This blessing was enacted in place of the thanksgiving offering that a woman used to bring to the Temple, and it is customarily recited during prayer services in the Synagogue, at the Simchat Bat ceremony, or anywhere that at least ten [adult] members of the community have convened.
בָּרוּךְ אַתָּה אֲדֹנָי אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם הַגּוֹמֵל לְחַיָּבִים טוֹבוֹת שֶׁגְּמָלַנִי כֹּל טוֹב
Barukh Atah Adonay Eloheynu Melekh Ha'olam, hagomel li-khayavim tovot shegamalni kol tov.
The new mother: Blessed are You, oh Lord, our God, King of the universe who bestows goodness upon the accountable, who has bestowed every goodness upon me.
מִי שְגָמָלֵך כֹּל טוֹב הוּא יִגְמְלֵךְ כֹּל טוֹב סֶלָה
Amen. Mi shegamalech tov, Hu yig'malech kol tov, selah.
Congregation: Amen, He who has bestowed goodness upon you, may He bestow every goodness upon you forever.