Shabbos 103a: One who writes two letters (on Shabbos) with the right hand or left hand is liable. A left-handed person is certainly liable for writing with his left hand, as his left hand is the equivalent to a right-handed person’s right hand. One who is ambidextrous is also liable for writing with either hand. With regard to the writing of two letters, there is no distinction between one who writes the same letter twice, i.e. aleph aleph, or if he wrote two different letters, i.e. aleph beis. If one wrote with ink and a different substance, he is also liable for writing on Shabbos. If one writes in any script used by any nation in the world one is liable for writing on Shabbos.
For most people, and indeed most animals as well (Chullin 91a), the right side of the body is more powerful. However, there are many people who differ from this norm, exhibiting greater strength and precision with their left hands. The Gemora refers to left-handed people as “ittar yad.” Ittar literally means closed or hindered. In this context, the phrase implies that the usually stronger hand, the right, is hindered from performing tasks with full strength (see commentaries on Shoftim 3:15).
1. Definition of a Left-Handed person
One that more powerful hand is the left and does most work with the left hand when requires strength. This applies whether born like this, or changed one’s nature later in life. The only exception is for the mitzvah of Tefillin, where the determining factor is which hand one uses for writing.
2. Definition of a Left-Footed person
One that more powerful foot is the left whether born such or changed later in life. General method to determine is which foot one starts when beginning to walk.
3. Definition of one who “rules with two hands” (ambidextrous)
One who displays power with either hand without distinction, whether born as such or trained later in life. Such a person has a legal status just like a “right-handed” person.
4. The primary method to do any mitzvah or Jewish custom is with the right hand due to importance (חשיבות)
When the metzora undergoes his purification process, a Kohen places olive oil and blood from a korban on the metzora’s right thumb, in his right ear, and on his right foot (Vayikra 14). From here, the Gemora (Menachos 10a) learns that the right side takes precedence to the left in regard to many other mitzvos of the Torah. A left handed person uses the left hand since that shows primary importance. If a right handed person has lost a portion of that hand, then anything that can be done with the right hand should be done with that hand; if not, then done with the left hand.
5. Any matter should have preference to be done with the right hand or side first
For example, getting dressed, putting on shoes. A left-handed person usually performs actions with the left hand or left side first due to the importance displayed with the more significant hand.
6. In all matters that display an allusion to the primacy of Chesed (right) before Gevurah (left)
No distinction depends whether the person if left or right handed.
7. All matters that involve internal organs do not have an effect on this issue.
8. Chabad (per the Tzemach Tzedek) decide the law according to the opinion (Rambam) that a left-handed status is considered a mum (defect).
Since most others establish the law per the other opinion (not considered a mum, just an inability to properly perform avodah correctly in the Bais haMikdash), this is the source of many differences between Chabad and the “standard” procedures.
9. Preparatory actions that are required to perform a mitzvah have the same status of importance to the right hand (see rule #4).
10. All laws regarding left and right hands applies equally to men or woman, unless noted otherwise.
11. No distinction in these laws whether the action is performed privately or in public settings.
For practical rules, see http://www.parshapages.com/Halacha/SUMMARY%20OF%20LAWS%20FOR%20THE%20LEFT%20HANDED.doc
