If you cannot use external APIs or dont want to, you can still use pure standard JDK API to access private methods using reflection. Here is an example
MyObject obj = new MyObject();
Method privateMethod = MyObject.class.getDeclaredMethod("getFoo", null);
privateMethod.setAccessible(true);
String returnValue = (String) privateMethod.invoke(obj, null);
System.out.println("returnValue = " + returnValue);
Check Java Tutorial http://docs.oracle.com/javase/tutorial/reflect/ or Java API http://docs.oracle.com/javase/7/docs/api/java/lang/reflect/package-summary.html for more information.
As @kij cited on his answer there are times when a simple solution using reflection is really good to test a private method.