You can find a detailed discussion of clothing in Pygmalion over in "Symbolism, Imagery, Allegory," but a couple more examples from the text can't hurt, right? Here's the description we receive of Henry Higgins at the beginning of Act 2:
He appears in the morning light […] dressed in a professional-looking black frock-coat with a white linen collar and black silk tie. (2.5)
What can we tell from this? Well, for one thing, Higgins doesn't mess around. He dresses neatly, "professionally," in a no-nonsense kind of way. His style is simple, a bit stark even, and it probably costs him a fair amount of money to pull it off. Silk isn't cheap after all. So there you have it: professional, no nonsense, wealthy…we can learn all that about Higgins just from his clothing.
Now, here's another case from later in Act 2:
Alfred Doolittle is an elderly but vigorous dustman, clad in the costume of his profession, including a hat with a back brim cover his neck and shoulders. (2.211)
This one's pretty straightforward: Doolittle's dressed like a dustman. Dustmen don't make much money. He is, at the very least, a blue-collar worker making a small amount of money, and at the worst living in true poverty. We learn more about him when he opens his mouth, but his clothing says a lot too.
Sometimes Shaw just likes to tell it like it is. His initial description of Higgins is a perfect example of this method:
He is in fact, but for his years and size, rather like a very impetuous baby "taking notice" eagerly and loudly, and requiring almost as much watching to keep him out of unintended mischief. His manner varies from genial bullying when he is in good humor to stormy petulance when anything goes wrong; but he is so entirely frank and void of malice that he remains likeable even in his least reasonable moments. (2.5)
There you have it: Higgins in a nutshell. There are a couple things to keep in mind, though. Pygmalion is a play, and the audience would not be reading this description. (That said, many of Shaw's plays were distributed to be read and were only performed some years after their writing.) Also, Shaw does not simply tell us these things. We get to know Higgins, and we get to see him act in precisely this way over the course of the play. He is not simply telling because he doesn't know how to show in action. He just wants to make sure that we get it.
Education in Pygmalion is most clearly reflected through speech. It is very easy to see who's educated and who's not in this early exchange between Eliza and Higgins:
THE FLOWER GIRL [far from reassured] Then what did you take down my words for? How do I know whether you took me down right? You just show me what you've wrote about me. [The note taker opens his book and holds it steadily under her nose, though the pressure of the mob trying to read it over his shoulders would upset a weaker man]. What's that? That ain't proper writing. I can't read that.
THE NOTE TAKER. I can. [Reads, reproducing her pronunciation exactly] "Cheer ap, Keptin; n' haw ya flahr orf a pore gel. (1.66-7)
Higgins can write in his strange way, read it back, and mimic other people's accents perfectly. Eliza can't even speak in a grammatically correct manner.
As usual, a look at Higgins will suffice. At the end of Act 2, Mrs. Pearce reprimands Higgins, warning him that he'd better clean up his act before he has a bad influence on Eliza:
MRS. PEARCE. Yes, sir. Then might I ask you not to come down to breakfast in your dressing-gown, or at any rate not to use it as a napkin to the extent you do, sir. And if you would be so good as not to eat everything off the same plate, and to remember not to put the porridge saucepan out of your hand on the clean tablecloth, it would be a better example to the girl. You know you nearly choked yourself with a fishbone in the jam only last week. (2.188)
That pretty much says it all. It also confirms a lot of what Shaw tells us about Higgins in his initial description (see above). Higgins really does act like a child.
OK, this one's easy to miss, and requires some knowledge of London geography to understand, but it deserves to be pointed out. At the end of Act 1, Eliza tells the cab driver to take her to "Angel Court, Drury Lane" (1.150). Yes, Drury Lane is where the Muffin Man lives, but, as it turns out, he doesn't live in a very nice neighborhood. Higgins and his mother, on the other hand, live in luxurious central London. You can read more about that under "Setting."
One word: Doolittle. Now, split it into to two words: Doo…Little. Get it? Not exactly subtle, but it does do a pretty good job describing Eliza's father. He's all talk and no rock, as it were. We also learn a lot just from the fact that Colonel Pickering is Colonel Pickering, instead of just Mister Pickering. It gives him a more dignified, disciplined air. Oh, and Eynsford Hill? That just screams wealthy British person, no?
OK, let's go through the main characters one by one. Henry Higgins: Phonetician and Speech teacher. Eliza Doolittle: Flower Seller (not, florist, mind you). Colonel Pickering: High-ranking military officer. Alfred Doolittle: Dustman. Freddy: Who knows? Nonetheless, it's clear just by looking at their job titles (if they even have any), what kind of person they are, how wealthy, etc.