Preponderance of Evidence means any amount of evidence greater than 50%. This is a term of art, which basically means that whomever produces the better case to the jury is supposed to win. In reality, convincing the jury is the real art, and the most convincing attorney is likely to win, no matter what the facts are.
Prima Facie Case means to produce evidence proving each element of the discrimination claim. This is actually a fairly low burden of proof
: (1) plaintiff/employee is a member of a protected class (race, color, nationality, religion, sex, age or disability); (2) plaintiff was qualified for a particular employment opportunity; (3) defendant/employer made an adverse employment decision concerning plaintiff; (4) plaintiff was damaged by defendant's actions.
As far as how someone wins -- it's all about proof. It's not always easy, unless there is either a document by management personnel evidencing discrimination, or a coworker is willing to testify to the fact that employer has discriminated. Getting an employee to "rollover" in favor of the employee is very difficult -- because employees are always in fear of being fired, even if they are protected by law from retaliation.
This is simply the way it is, and it's why so few cases are brought to court. They are difficult to win -- despite the low bar, due to the typical lack of written or testimonial evidence against the employer.
But, that's the system and the law, so, if you want to win, then you need proof, and frequently, getting that proof can be a very daunting task.
Hope this helps.