Not only is the question complex, but the answer is too! Most opinions rule that the defining criterion is writing, whether that makes his a “righty” or a “lefty”. A minority opinion rules that we must take the other skills into account as well. In practice, the Mishnah Berura concludes – in light of the fact that an ambidextrous person is also regarded as a righty – that unless a person is a pure “lefty”, he should put on tefillin like a “righty”. (Ed: If you or your son falls into one of these “questionable” categories, you might want to consult your rav for clarification. After all, remember what we learned above, that if one puts tefillin on the wrong hand, he has not fulfilled the mitzvah!)
.The universal custom is to wrap the retzua (strap) of the ‘shel yad’ about seven times around the forearm, and three times around the middle finger. (Note: Actually, the three around the finger is required by halacha, and the seven around the arm is only ‘minhag’ - custom. Exact procedures vary according to tradition.) One should avoid wrapping the ‘retzua’ over the ‘ma’avarta’ (i.e. the wide part of the base of the ‘bayis’), because he would then be placing something of a lower level of ‘kedusha’ (holiness – i.e. the ‘retzua’) on top of something of a higher level of ‘kedusha’ (the ‘bayis’). If he needs to do this in order for the ‘bayis’ to remain tightly on his arm, then it is permitted.