A few thoughts from this (mostly) left-handed person who has done some looking in to the research on handedness (laterality).
From the full population, if there is no cultural hostility to left-handedness and hasn't been for 2+ generations, about 10% of the population is left-handed. It is, however, much more accurate to view handedness on a spectrum, rather than a binary matter. Most left-handed people don't do absolutely everything left-handed (I throw right-handed, for instance), and even many right-handed people don't do everything that way either.
There does seem to be a genetic component, but it is neither terribly strong, nor is it simple like blue eyes vs. brown eyes. Among lefties, left-handed women tend to be more strongly left-handed than leftie men. There may be somewhat fewer (percentagewise) left-handed women than men. It's debated as to whether this is nature or because of the acculturation of women.
Various realms of activity show increased fractions of lefties -- math, natural science, art, music, and sports. The increase is higher the higher you go in each field, i.e., only somewhat over 10% at the undergraduate math level, high teens/low 20s for graduate students, mid-upper 20s for postdoctoral, and about 30% for the senior professional mathematicians. 30% seems the general highest level, and is also common to sports and science (at least).
The preceding is why a particular study I read that claimed correlation between left-handedness and homosexuality was a piece of crap. In order to have a large enough homosexual population to look in to handedness, the authors checked memebers of a lesbian volleyball league. Found increased (over general population) percentage of lefties. But they ignored entirely that the same thing would have happened if they'd checked a straights-only volleyball league.