To prove a case of reverse discrimination you should typically begin by considering the case as one of discrimination in general, and not as reverse discrimination. This means you need to be able to indicate that there was an incident of discrimination against you due to a particular aspect of who you are that is protected by the laws of your country or region. In the US, for example, you cannot be discriminated against in certain situations based on your race, gender, religion, or any physical disabilities. Efforts to prove reverse discrimination can be stymied by semantics over the term itself, so it is often best to not use the term if possible.
Reverse discrimination is typically considered to be any form of discrimination targeted against the majority or controlling group within a particular segment of society. In the US, for example, white men have typically been seen as the majority and controlling group within society. Reverse discrimination in the US, therefore, is typically seen as discrimination aimed at white men. This can quickly become a controversial subject, however, and so it is often easiest to approach such an incident merely as discrimination without any other labels.
To prove a discrimination case, you typically need to prove that you were the target of action or inaction that you should otherwise not have been, due to some aspect of who you are that cannot be used as the basis of such a decision. For example, if you were not hired by a company or you were passed over for a promotion due to your race or gender, then you have been the victim of discrimination. Laws in the US and many other countries do not indicate what genders or races are protected from discrimination, only that such attributes cannot be used for making certain decisions.
You typically need to have evidence that demonstrates an action or inaction was taken, and that it was based on a certain attribute of your personality that cannot be the basis for discrimination. This means you need to be able to prove that you were actually passed over for a promotion, that you were not hired by a company, or that you did not receive a home loan. Furthermore, you must be able to prove that this occurred because of your gender, race, disability, or similar attribute. Regardless of whether you are trying to prove discrimination or reverse discrimination, you should also try to find witnesses or documents that support your claim.