Depending on why the application was denied, you can re-apply. You will have to complete and resubmit a new N-400 and pay the fee again. You will also need to have your fingerprints and photographs taken again. If your application is denied, the denial letter should indicate the date you may reapply for citizenship. If you are denied because you failed the English or civics test, you may reapply for naturalization as soon as you want. You should reapply whenever you believe you have learned enough English or civics to pass the relevant test.