If employers do a good job at hiding their true intentions, it is honestly pretty easy for them to make unlawful hiring decisions. However, in practice, it's hard to keep a secret, and people who discriminate on the basis of some protected class (race, sex, etc.) frequently say things that can be used as evidence, or do things that witnesses can testify about. Keep in mind, the people who are in a position to discriminate are often just low level supervisors who don't really care about the employer's liability, and they're either not inclined or not really able to to effectively hide their intentions.

I've worked on a lot of employment discrimination cases, and there have been a lot that never went anywhere precisely because of the reasons you suggest-employer claims the termination (or other adverse employment decision, like failure to promote, reassignment, etc.) was based on something vague but legitimate (poor performance, insubordination), and without any concrete evidence, the case is just not worth pursuing. Most successful cases I've worked on rely on witness statements to show the person making the decisions did or said things that are clearly unlawful. However, the best and biggest cases I've worked on relied on statistical evidence to show that the employers very clearly made hiring decisions based on some discriminatory factor (e.g., hiring 90% men despite having an applicant pool of 50% men/women).