That heavily depends on whether you want to launch it as a separate process or simply execute within the same one.
To kick it off in the same process, you could just call the main method:
String[] arguments = new String[]{"-option1", "<option>", "<a string value>"};
MyOtherMainClass.main(arguments);
To start it as a different process:
ProcessBuilder pb = new ProcessBuilder("java", "-jar", "<my jar name>.jar", "-option1", "<option>", "<a string value>");
Process process = pb.start();
int errCode = process.waitFor();
The second example was inspired by http://examples.javacodegeeks.com/core-java/lang/processbuilder/java-lang-processbuilder-example/
mainmethod with the relevant arguments?