Even if you decide not to challenge the legality of your firing, you will be in a much better position to enforce all your workplace rights if you carefully document what happened when you were fired. For example, if you apply for unemployment insurance benefits and your former employer challenges your unemployment application, you will typically need to prove that you were dismissed for reasons that were not related to your own misconduct. (For more information, see Nolo's article Unemployment Benefits: What If You're Fired?)
First, ask to see your personnel file. In many states, employers are required to make it available to you. Make a copy of all reports and reviews in it. Again, some states require the employer to allow you to make copies. Make a list of every single document the file contains. That way, if your employer adds anything later, you will have proof that it was created after the events in question. (For tips on checking your file, see Your Personnel File and Your Rights.)
There are a number of ways to document events that happened. The easiest is to keep a journal in which you record and date significant work-related events such as performance reviews, commendations or reprimands, salary increases or decreases, and even informal comments your supervisor makes to you about your work. Note the date, time, and location for each event; which members of management were involved; and any witnesses who were present. Keep your notes at home or in a secure place.
Whenever possible, back up the notes in your journal with materials issued by your employer -- such as copies of the employee handbook; memos; brochures; employee orientation videos; and any written evaluations, commendations, or criticisms of your work. However, don't take or copy any documents that your employer considers confidential -- this will come back to haunt you if you decide to file a lawsuit. For information on documenting your situation, see Nolo's article Wrongful Termination: Gathering Documentation.