How do you write a request for time served?

You do not write a request for time served. You need to write a motion to put a motion before the court. You must be in jail or prison. Do you have access to a law library? You need someone to guide you through the process. Why do you think you should get off with time served? Do you have a good reason? If you have some sort of good reason, a motion exists for your purpose. You should be able to copy it out of a book and list your reasons in the proper place. Then you should send it to the proper court, probably the one that sentenced you in the first place. Your state may have special rules. Use them. If all goes well, the judge will review your motion. If all goes even better, the judge will call you to come back to court to answer some questions. The prosecutor might give you a dressing down to get you all confused. Still, some prisoners get relief.