When Theodor Herzl prepared to open the first World Zionist Congress, the international gathering that would change Jewish history, his greatest worry was being called to the Torah the preceding Shabbat. I suspect his experience is not so different from yours, so to help allay that concern, I offer this concise guide to having an aliya.
While you may think the customs you learned in other circumstances are authoritative, I assure you that what follows is what halakha prescribes. And while I stop short of insisting on uniformity, I hope this column resolves unnecessary debates over the "right" way to fulfill this great honor.
You should take the most direct route to the bima upon hearing your name called. Standing to the right of the reader (unless, of course you are the reader), you lightly touch the first word of your portion with the corner of your tallit, then kiss the corner. (Everyone called to the Torah should wear a tallit, but if you will not, then you may use the reader's tallit or the belt from the scroll.) You grip the handles of the scroll with the column from which the reading begins visible (yes, that is correct). Looking away from the Torah so as not to give the impression you are reading from the text, you recite "Barkhu..." and wait for the congregation's response. Repeat that response and continue with the first brakha.
The congregation and then the reader (unless it is you) will answer "amen." Then, you should follow the actual reading from the scroll while holding the handle closest to you.
When the reading is completed, touch and kiss the last word (as before) and, holding both handles again, roll closed the scroll. Recite the last brakha. When you finish, step to the right and remain in place through the next aliya.
You will be greeted with some version of "yasher ko 'ach" (that's another column!), to which the proper response is "barukh ti'h'yeh" (to a male) or "brukha ti'h'yi" (to a female). Take an indirect route back to your seat (greeting the hazzan and the rabbi is always appreciated!).
Sephardic custom is to precede Barkhu with words from the Book of Ruth, "Adonai imakhem," to which the congregation responds "Y'varekh'kha Adonai." The second brakha is preceded with the word, "Emet," meaning "Truth."
In a future column, I will try to clear up the variations in lifting, wrapping and carrying the Torah. But for now, take satisfaction that you can have more confidence in coming to the Torah than the founder of modern Zionism!