R' Paysach Krohn wrote an English-language book on halachos for lefties. It's available free by mail if you call his home; he lives in Queens, New York, and is listed. (Obviously, you might want to pay him for it, and the postage.) It's also online. (Thanks to Dr. Melech Tanen for linking to it.)
The book is arranged in sections, one of which is a list of things lefties do the same as righties, and another of which is things lefties do the opposite from the way righties do; so one whole section of that book answers your question. It contains fourteen subsections:
- A left-handed person holds a food or mitzva item in his left hand while saying the b'racha on it;
- some say that's true of a cup of wine held during birchas hamazon also;
- it's true of the lulav also.
- A kidushin ring is given by the left hand of a left-handed bridegroom, and/or to the left hand of a left-handed bride. (See the book for exceptions.)
- A left-handed person steps back after sh'mone esre starting with his right foot;
- take a sefer Tora with his left hand;
- and possibly hold the chicken for kaparos with his left hand.
- It's unclear whether he should burn chametz (and do similar activities (see the book)) with his left hand.
- A left-handed man wears his t'fila shel yad on his right arm,
- removes his t'fila shel rosh with his right hand,
- and puts his shel yad on the left side of his t'filin pouch.
- A left-handed sofer uses his left hand to write.
- A left-handed man wearing t'filin does n'filas apayim on the arm without t'filin: the left.
- A left-handed person ties his right shoe before the left one, and unties it after the left one.
But consult your own rabbi for practical rulings.