Actually a guy at the Bimah, which is the table where the Torah is read will say: “Ya’amod (which means Stand up) Mr. so and so son of so and so.” He will usually look in your direction while he says this to give you a heads-up. At that point you make your way to the bimah and stand on the right side of the Torah reader with your back to the congregation. You may have to just stand there for a minute or two while some blessings are said for the previous guy who got called up. When those blessings are finished, the Torah reader will point to the spot(s) in the Torah that he will read from and you are to touch the Torah in that spot(s) with the edge of your Tallit and then kiss the tallit. (Some congregations don’t do this and just go straight for the blessing. Some congregations touch only the beginning and some touch both the beginning and end. In Chabad synagogues the custom is touch both the beginning and end.)

Take hold of the Torah’s wooden handles and recite the following aloud (in Chabad synagogues roll the Torah closed before reciting the blessing):

"Bor-chu et ado-nai hamvorach."

(Pause about 4 seconds and continue:)

"Boruch ado-nai hamvorach l’olam vo’ed."

"Boruch attah ado-nai

Elo-heinu melech ha’olam

Asher bachar banu mikol ha’amim

Vinatan lanu et toroto

Baruch attah ado-nai

Notein hatorah."

Now the Torah reader will begin reading the Torah and you just stand there looking in to the Torah. Look at the words even if you can’t read them. They’ll have a good effect on you.

When the reader is finished, you will kiss the Torah again with the tallit, then recite the following (in Chabad synagogues roll the Torah closed before starting the blessing):

"Boruch attah ado-nai

Elohei-nu melech ha’olam

Asher nattan lanu torat emet

Vi’cha’yei olam

nattah bitocheinu

Boruch attah ado-nai

Notein hatorah."

You’re done. But don’t go back to your seat just yet. Stand on the right side of the bimah throughout the next Aliyah and return to your seat after the next guy has finished his second blessing.

Right after you finish the blessing, the next person is called up. Then, the guy who called you up may start saying a prayer and in the middle ask you for your name and father’s name again. What he’s doing is saying a beautiful prayer for you in honor of your aliyah. At the end of the prayer you and the whole congregation will say amen. (If you want to make a contribution to the synagogue, make mention of it during this prayer and they will add it into the prayer by saying “and in the merit of his donation of 1,000,000 dollars…” This prayer is called a Mee she’bay’rach.)

When returning to your seat, go around the bimah. Some people may extend a hand to you or just say yasher koach, [Read about "What is the meaning of "Yasher Koach"?'] which is a blessing and you can respond by saying “thank you.” (If you want to get fancy, you can respond with “bruchim tee’yu” which means “may you be blessed.”)

Wipe sweat from brow.