Depending on your type of case and how fast it's approaching, you may be able to postpone your court date. You should check with the court clerk to find out your court's procedures for requesting an adjournment. If you write a letter, address it to the judge and explain why you need a new date.
The process for extending court dates vary. In some jurisdictions, you may have to file a motion for continuance. Some courts do not accept letters, so a simple letter will not suffice in those cases. However, if you have been instructed by the court to write a letter for your request, there are some things you should include. The letter should be professional and typewritten. It also should be sent to the court with plenty of time to reschedule your hearing.
TL;DR (Too Long; Didn't Read)
If your jurisdiction permits an adjournment or continuance of a court hearing by letter request, you should contact the clerk's office for the court procedure, and then write a letter addressed to the judge explaining why the scheduled date doesn't work for you.
Do Your Research on Local Procedure
Call or visit the clerk of the courts to find out the procedure for obtaining a new court date. Ask if you need to file a motion for continuance or if a letter will work. Also, ask about any fees. Remember that you may or may not be allowed to file for a postponement depending on the type of court case and how soon to your court date is approaching. If your hearing is tomorrow, for example, a judge is unlikely to grant your request unless you have an emergency.
Formatting the Letter: the Introduction
Format your letter as a business letter. Include your address and date on top of the letter. Put the judge’s name (written as "Honorable <First Name> <Middle Initial> <Last Name>") and the court’s address underneath the date in your letter. Include a memo line with your case number and the caption of the case (i.e., John Smith vs. Jane Doe). Then, address the letter to the judge who is overseeing your case by writing "Dear Judge <Last Name>:" Don't forget to include your request for continuance in the opening paragraph.
Formatting the Letter: The Explanation
Specify the reason you are asking for an extension in the next paragraph. You may want to include how long of an extension you feel you need. Remember to go into as much detail as possible, as it will help the court decide whether or not to grant the postponement.
Formatting the Letter: Closing
Close your letter with contact information so the court may inform you of a new hearing date, if granted. Sign off on the letter with the closing, "Respectfully submitted," and then a space for your signature, and then your typed name. Sign your letter in that space after proofreading the letter and correcting any mistakes in spelling, grammar or punctuation.
Things to Remember
It's prudent to make a few copies of the letter before mailing, faxing or delivering it to the court. Ask the clerk which the other party (if your case is a civil matter) and keep a copy for your records.
Don't forget to check with the clerk of the courts before your hearing date if you do not hear a response. You do not want to be in contempt of court for missing your original hearing date if no new date is set.