File mydir = context.getDir("mydir", Context.MODE_PRIVATE); //Creating an internal dir;
File fileWithinMyDir = new File(mydir, "myfile"); //Getting a file within the dir.
FileOutputStream out = new FileOutputStream(fileWithinMyDir); //Use the stream as usual to write into the file
Для удаления файла из внутреннего:
if (new File("path/to/file").delete()) {
// Deleted
} else {
// Not deleted
}