In the original books, Adrian Veidt attributes his own powers to training and discipline. An interview Veidt gave to Nova Express is included at the end of Chapter XI:
NOVA: So, how do you get to be a superhero? ...
VEIDT: ... To answer your question, you get to be a superhero by believing in the hero within you and summoning him or her forth by an active will. Believing in yourself in your own potential is the first step to realizing that potential. ...
NOVA: You'll forgive me for saying so, but isn't that philosophy a little bit Norman Vincent Peale? That self-realization stuff? How exactly do you exploit the potential to the degree that you obviously have?
VEIDT: The disciplines of physical exercise, meditation and study aren't terribly esoteric. The means to attain a capability far beyond that of the so-called ordinary person are within reach of everyone, if their desire and will are strong enough. I have studied science, art, religion and a hundred different philosophies. Anyone could do as much. By applying what you learn and ordering your thoughts in an intelligent manner it is possible to accomplish almost anything. Possible for the "ordinary person." There's a notion I'd like to see buried: the ordinary person. Ridiculous. There is no ordinary person.
In addition, some introductory text for a self-improvement book sold by Veidt, on the "Veidt Method", is included at the end of Chapter X. It also claims that discipline and study can turn anyone into a superhero:
Our third and longest chapter presents a carefully coordinated series of physical and intellectual exercise systems which, if followed correctly, can turn YOU into a superhuman, fully in charge of your own destiny. All that is required is the desire for perfection and the will to achieve it. No special equipment or other hidden cash extras are necessary. The Veidt Method paves the way for a bright and hopeful future in which anyone can be a hero.
As pointed out in the comments, it is entirely possible that these statements are not generally true. They could be puffery à la Charles Atlas, they could be an attempt at social engineering, or they could just not be generalizable (even if Veidt believes they are.) Given that Watchmen is something of a commentary on classic comic books, the implicit connection to Charles Atlas may well be intentional.