Be clear about what constitutes workplace discrimination. Discrimination is a broad word that covers a variety of acts. Employers can't make hiring, compensation or promotional decisions based on the details of a protected class, nor can they place employment-specific conditions or deny benefits based on a person's differences.
Determine whether you fall into a "protected class" of people covered by anti-discrimination laws. It is a federal violation to discriminate against people due to: race, ethnicity, religion, national origin, age, gender, disability, color, political affiliation or veteran or familial status. Though there are not federal anti-discrimination laws in place in regard to sexual orientation, many states and local jurisdiction have passed laws making it illegal.
Ask yourself whether you were treated differently than your equally qualified peers, subjected to derogatory remarks or placed in conditions which made it impossible to perform your job. Write down your answers to these questions and try to think of specific examples to support your feeling.
Look around the workplace to see whether the workforce is unusually homogeneous. This can be beneficial in proving discrimination. An employer who consistently hires employees outside of protected classes may be practicing discriminatory hiring practices.
Listen to what your coworkers have to say. Others may be experiencing the same type of discrimination or know of a former employee who was subjected to discrimination. They may be willing to work with you to prove your claim.
Gather as much direct evidence of discrimination as possible. While it's hard to prove discrimination based on subtle actions, having written statements or other evidence of discriminatory actions is concrete proof. Memos and notes of conversations are direct evidence, as are witnessed comments. For example, if a coworker hears your supervisor discouraging you from applying for a promotion because of your gender, this can be used as direct evidence.