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Perfect for beginners, this clear article from Chabad.org explains the origins behind being called up to the Torah, as well as when and how this is practiced in Orthodox congregations, including the Hebrew, English, and transliterated texts of the blessings recited both before and after the aliyah (also provided below).
The Text of the Blessings
Blessing before the reading of the Torah
Transliteration: Bor'chu es ado-noy ha-m'voroch.
Translation: Bless the L-rd who is blessed.
Congregation and Oleh say:
Transliteration: Boruch ado-noy ha-m'voroch l'olom vo-ed.
Translation: Blessed be the L-rd who is blessed for all eternity.
Oleh continues:
Transliteration: Boruch atoh ado-noy elo-haynu melech ho-olom, asher bochar bonu mikol ha-amim, v'nosan lonu es toroso. Boruch atoh ado-noy, nosayn ha-toroh.
Translation: Blessed are You, L-rd our G‑d, King of the universe, who has chosen us from among all the nations and given us His Torah. Blessed are You L-rd, who gives the Torah.
During the Aliyah hold the right handle of the Torah, and read quietly along with the Reader.
At the conclusion of the Aliyah touch the end and beginning of the Torah reading with the corner of your Tallit (or the Torah's sash) and kiss it. Close the Torah, hold both handles, turn the head slightly to the right and say:
Blessing after the reading of the Torah
Transliteration: Boruch atoh ado-noy elo-haynu melech ho-olom, asher nosan lonu toras emes, v'cha-yay olom nota b'sochaynu. Boruch atoh ado-noy , nosayn ha-toroh.
Translation: Blessed are You, L-rd our G‑d, King of the universe, who has given us the Torah of truth and planted eternal life within us. Blessed are You L-rd, who gives the Torah.
After the Aliyah stand on the right side of the podium until the end of the following Aliyah (if it was the last Aliyah — until the Torah is raised). When returning to your seat do not use the shortest route.
Note: Not experienced? Don't worry. The gabbai will guide you through the process!