If your F1 visa application is denied, it is based on US immigration law. It is important to understand why you were denied, the reason and section of law you are denied under will be given to you in your paperwork.
Some applications are denied because the applicant failed to provide necessary information or supporting documentation as required. Sometimes, however, you can be found ineligible for other reasons.
If the reason you have been denied is a fixable problem, then reapply making sure you resolved the exact issue that caused your denial in the first application.
Common reasons for denial include:
Fraud or Misrepresentation
Unlawful Presence in the United States
Lack of financial proof to support your education and life in the USA
Health-related grounds
Criminal-related grounds
The consular officer is not convinced or does not have documented proof of your intent to go back to your home country after completion of education.
Keep in mind that there is not an appeal process, but reapplying is an option.
To learn more about visa denials and to see if you are eligible for a waiver or to reapply, the US Department of State website is a great resource.