You could do something like this, get your application directory
String pathToExternalStorage = Environment.getExternalStorageDirectory().toString();
File appDirectory = new File(pathToExternalStorage + "/" + "AppName");
// have the object build the directory structure, if needed.
appDirectory.mkdirs();
Now this creates a custom directory on external storage as the android docs says..
If you want to save files that are not specific to your application and that should not be deleted when your application is uninstalled, save them to one of the public directories on the external storage. These directories lay at the root of the external storage, such as Music/, Pictures/, Ringtones/, and others.
EDIT:
Use Context.getDir(String name, int mode) method to create or access directories in internal storage. Quote from docs:
Retrieve, creating if needed, a new directory in which the application
can place its own custom data files. You can use the returned File
object to create and access files in this directory. Note that files
created through a File object will only be accessible by your own
application; you can only set the mode of the entire directory, not of
individual files.
Example:
File mydir = context.getDir("mydir", Context.MODE_PRIVATE); //Creating an internal dir, set it to private so its only visible to our application;