You should have bothered to do a bit of searching before posting. StackOverflow.com has many questions and answers like this already.
But for the sake of posterity, here's some example code using the Joda-Time 2.3 library. Avoid the java.util.Date/Calendar classes bundled with Java as they are badly designed and implemented. In Java 8, continue to use Joda-Time or switch to the new java.time.* classes defined by JSR 310: Date and Time API. Those new classes were inspired by Joda-Time but are entirely re-architected.
Joda-Time has many features aimed at formatting output. Joda-Time offers built-in standard (ISO 8601) formats. Some classes render strings with format and language appropriate to the host computer's locale, or you can specify a locale. And Joda-Time lets you define your own funky formats as well. Searching for "joda" + "format" will get you many examples.
// © 2013 Basil Bourque. This source code may be used freely forever by anyone taking full responsibility for doing so.
// import org.joda.time.*;
// import org.joda.time.format.*;
String input = "05/27/2014" + " " + "23:01";
Parse that string…
// Assuming that string is for UTC/GMT, pass the built-in constant "DateTimeZone.UTC".
// If that string was stored as-is for a specific time zone (NOT a good idea), pass an appropriate DateTimeZone instance.
DateTimeFormatter formatterInput = DateTimeFormat.forPattern( "MM/dd/yyyy HH:mm" ).withZone( DateTimeZone.UTC );
DateTime dateTime = formatterInput.parseDateTime( input );
Ideally you would store the values in an appropriate date-time format in a database. If not possible, then store as a string in ISO 8601 format, set to UTC/GMT (no time zone offset).
// Usually best to write out date-times in ISO 8601 format in the UTC time zone (no time zone offset, 'Z' = Zulu).
String saveThisStringToStorage = dateTime.toDateTime( DateTimeZone.UTC ).toString(); // Convert to UTC if not already in UTC.
Do your business logic and storage in UTC generally. Switch to local time zones and localized formatting only in the user-interface portion of your app.
// Convert to a localized format (string) only as needed in the user-interface, using the user's time zone.
DateTimeFormatter formatterOutput = DateTimeFormat.mediumDateTime().withLocale( Locale.US ).withZone( DateTimeZone.forID( "America/New_York" ) );
String showUserThisString = formatterOutput.print( dateTime );
Dump to console…
System.out.println( "input: " + input );
System.out.println( "dateTime: " + dateTime );
System.out.println( "saveThisStringToStorage: " + saveThisStringToStorage );
System.out.println( "showUserThisString: " + showUserThisString );
When run…
input: 05/27/2014 23:01
dateTime: 2014-05-27T23:01:00.000Z
saveThisStringToStorage: 2014-05-27T23:01:00.000Z
showUserThisString: May 27, 2014 7:01:00 PM