Almost. In theory anyone has the potential to become an Esper given sufficient effort. In practice, there are plenty of people who go through the Power Curriculum Program and awaken no ability. The question of whether they simply didn't try hard enough or lack something essential to the process is open for debate.
According to the (fairly vague) source material it's usually a mixture of physical training, mental examinations, hypnosis, ordinary lessons and machine-aided stimulation. In the case of a particularly promising Esper more unsavory methods may be secretly used as well; The government of Academy City aren't above risking their students' lives if it creates a more powerful weapon for them to use.And what hard work would that be exactly?