Written warnings and their penalties vary depending on your state or even local laws. In some states a written warning is actually a ticket that says the person named must pay a fine or appear in court. In some states, such as California, there is typically a fee to be paid and the warning gives you a 1 point infraction on your driving record.
Some states allow for a written warning to not carry a fine or require a court appearance but merely serve as a reminder that you are driving too fast. There are states that do this and keep the warnings listed in a database so that repeat offenders will be identified and ticketed if they are stopped within a certain time period.
To find out what your state or locality requires you to do regarding a written warning contact your department of motor vehicles. They should be able to give you the specifics of what your next step should be.