Use getDir(String name, int mode) to create directory into internal memory. The method 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.
So example is
// Create directory into internal memory;
File mydir = context.getDir("mydir", Context.MODE_PRIVATE);
// Get a file myfile within the dir mydir.
File fileWithinMyDir = new File(mydir, "myfile");
// Use the stream as usual to write into the file.
FileOutputStream out = new FileOutputStream(fileWithinMyDir);
For nested directories, you should use normal java method. Like
new File(parentDir, "childDir").mkdir();
So updated example should be
// Create directory into internal memory;
File mydir = getDir("mydir", Context.MODE_PRIVATE);
// Create sub-directory mysubdir
File mySubDir = new File(mydir, "mysubdir");
mySubDir.mkdir();
// Get a file myfile within the dir mySubDir.
File fileWithinMyDir = new File(mySubDir, "myfile");
// Use the stream as usual to write into the file.
FileOutputStream out = new FileOutputStream(fileWithinMyDir);