This varies greatly depending on the type of case. In most cases, you will need to file with the EEOC before you can file a lawsuit. The EEOC keeps your file for up to 6 months (sometimes longer, if I agree - which is rare).
After the EEOC releases your file, they will give you a "Notice of Right to Sue," which allows you to move forward in court. Once you file in court, it will be 1 to 2 years before you get to trial. Employment litigation is a long process. From the date of termination or other wrongful act, until the date of trial, it's often over 2 years.