How does the idea that each individual must make the best of the life he is given work in Shaw's Pygmalion?
Shaw loved to poke fun at society and its prejudices. Pygmalion, loosely based on the myth of Pygmalion (Book Ten of Ovid's Metamorphosis), demonstrates that social class is not necessarily permanent, and that rich or poor, people are people.
The idea that individuals have to just accept their lots in life is opposite of Shaw's theme. Eliza was a poor flower-girl whose accent kept her from getting a proper education and a real job. British society would keep her there, saying that she must make the best of her circumstances, but there is no way to break out of that class. Professor Higgins proved otherwise by teaching Eliza a more upper class way of speaking--and she was accepted by the upper class as one of their own. Eliza was not "stuck" in the lower classes of London, but could (and did) work her way up.
The same is true in modern culture. Just because someone is born into bad circumstances does not mean that he or she has to stay that way. Hard work and commitment can give any individual the possibility of great success.