How did one become a Wizard in A Wizard of Earthsea? Is magic basically just a skill that anyone could theoretically acquire with study, or did one have to be born with certain abilities before you even had the theoretical capability of learning to use it (like in the Harry Potter series)? What's to stop "ordinary" people from studying things like True Speech and using them successfully?
In the essay ‘A Description of Earthsea’, included in Tales of Earthsea, Le Guin writes:
Among the Hardic-speaking people of the Archipelago, the ability to do magic is an inborn talent, like the gift for music, though far rarer. Most people lack it entirely. In a few people, perhaps one in a hundred, it is a latent, cultivable talent. In a very few people it is manifest without training.
which would appear to answer the question, but I prefer to take a different view of the matter, by looking at the way the characters describe their world. (“Infinite are the arguments of mages,” as Vetch says in A Wizard of Earthsea.)
Two words that are used many times by characters in the Earthsea novels to describe magical abilities are skill and power (or, less often, strength). The word power in particular occurs more than a hundred and thirty times in A Wizard of Earthsea alone. What exactly the speakers mean by these words is hard to know, but they often appear together as if opposed or contrasted:
“He has either skill or power, or the doorkeeper wouldn’t have let him in. Why shouldn’t he show it, now as well as later? Right, Sparrowhawk?” [A Wizard of Earthsea chapter 3]
“I have both skill and power,” Ged said. [AWoE chapter 3]
She spoke now very softly. “Benderesk is Lord and Inheritor of the Terrenon, but he cannot use the thing, he cannot make it wholly serve his will. Nor can I, alone or with him. Neither he nor I has the skill and power. You have both.” [AWoE chapter 7]
“Because every instant since I set foot in the cavern under the Tombstones, I have striven to keep them still, to keep them unaware. All my skills have gone to that, I have spent my strength on it.” [The Tombs of Atuan chapter 9]
“I have no skill, I don’t think I have any power, but there were mages among my forefathers” [The Farthest Shore chapter 1]
“Would you have your power back, the skills, the names? I can give you that.” [TFS chapter 6]
With all the skill of his life’s training and with all the strength of his fierce heart, Ged strove to shut that door, to make the world whole once more. [TFS chapter 12]
Like any wizard, Ogion had been supported by the people his skills and powers served [Tehanu chapter 7]
There were men of great skill and power in Losen’s pay. [‘The Finder’, Tales of Earthsea]
A few wizards had crossed his path strong enough to make him wary of them, but he had never known one with skill and power equal to his own. [‘The Finder’]
Of these two attributes, power seems to be something innate:
When she found that he knew nothing, and yet had spellbound the goats to come to him and follow him, then she saw that he must have in him the makings of power. [AWoE chapter 1]
“He lived in Havnor. They accounted him a mere sorcerer, but in native power he was a great mage.” [TFS chapter 5]
For he had hoped—from the very beginning he had hoped—that the reason the Archmage had chosen him and him alone for this voyage was that he had some inborn power, descended from his ancestor Morred, which would in the ultimate need and the blackest hour be revealed [TFS chapter 9]
Whereas skill seems to be something learned:
So bolstering up his pride, he set all his strong will on the work they gave him, the lessons and crafts and histories and skills taught by the grey-cloaked Masters of Roke [AWoE chapter 3]
But Jasper said only, “When I have learned skills worthy of my Masters here and worthy of your praise, my lady, then I will gladly come” [AWoE chapter 3]
The key thing to note is in the very first quotation given above, “He has either skill or power, or the doorkeeper wouldn’t have let him in”. The Master Doorkeeper decides whom to admit as a pupil to the School of Wizardry on Roke, so the implication is that either skill or power suffices to enter the School, that is, innate power is not necessary to study magic. Of course, this is a line of dialogue, and the speaker (Jasper) may not be right. But bolstering this implication is the lack of mention in the Earthsea novels of anyone being innately incapable of magic: this suggests that there is no equivalent of the ‘muggles’ in the Harry Potter novels. So I prefer to imagine that ‘A Description of Earthsea’ is incorrect, and the people of Earthsea are innately endowed with varying aptitude for magic, not ability.
Gareth Rees's answer covers the most important points, i.e. how to become the sort of wizard that the school of Roke approved of. The last novel in the Earthsea cycle, The Other Wind, mentions that there is another category of wizards in the world of Earthsea. One of the people at Lebannon's court is Seppel, a wizard from Paln, whom many people try to avoid (my emphasis):
Paln, the greatest island west of Havnor, had the reputation of being an uncanny place. The Pelnish spoke Hardic with a peculiar accent, using many words of their own. (...) Their wizards did not go to Roke for their training. The Pelnish Lore, which called upon the Old Powers of the Earth, was widely believed to be dangerous if not sinister. Long ago the Grey Mage of Paln had brough ruin on his island by summoning the souls of the dead to advise him and his lords, and that tale was part of the education of every sorcerer: “The living should not take counsel of the dead.” (…) And fifteen years ago, when the wizard Cob had used the Pelnish Lore to cross between life and death, the Archmage Sparrowhawk had spent all his own power to defeat him and heal the evil he had done.
(The wizard Cob is a character in The Farthest Shore.)
However, the book does not provide any details about how potential wizards are discovered or how they get their training.