You can get your working folder by calling the method getFilesDir() on your Activity (Activity is the central class in your application that inherits from Context. See here). Reading is not different. Only your application will have access to this folder.

Your activity could contain the following code, for instance:

  File myFolder = getFilesDir();
  File myFile = new File(myFolder, "myData.bin");

  File myFile = new File(getFilesDir(), "myData.bin");
  FileOutputStream out = new FileOutputStream(myFile);

  // Write four bytes one two three four:
  out.write(new byte [] { 1, 2, 3, 4}
  out.close()

There is nothing Android specific with this code. If you write lots of small values often, use BufferedOutputStream to reduce the wear of the device internal SSD.

The old good Java object serialization is available for you in Android. you can define Serializable classes like:

  class Cirle implements Serializable {
    final int radius;
    final String name;

    Circle(int radius, int name) {
      this.radius = radius;
      this.name = name;
    }
  }

and then write then to the ObjectOutputStream:

  File myFile = new File(getFilesDir(), "myObjects.bin");
  FileOutputStream out = new FileOutputStream(myFile);
  ObjectOutputStream oout = new ObjectOutputStream(new BufferedOutputStream(out));

  oout.writeObject(new Circle(10, "One"));
  oout.writeObject(new Circle(12, "Two"));
  
  oout.close()

Java object serialization may be either perfect or really bad choice, depending on what do you want to do with it - outside the scope of this tutorial and sometimes opinion based. Read about the versioning first if you decide to use it.

You can also read and write from/to memory card (SD card) that is present in many Android devices. Files in this location can be accessed by other programs, also directly by the user after connecting device to PC via USB cable and enabling MTP protocol.

Finding the SD card location is somewhat more problematic. The Environment class contains static methods to get "external directories" that should normally be inside the SD card, also information if the SD card exists at all and is writable. This question contains valuable answers how to make sure the right location will be found.

Accessing external storage requires permissions in you Android manifest:

<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
<uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />

For older versions of Android putting permissions it is enough to put these permissions into manifest (the user must approve during installation). However starting from Android 6.0 Android asks the user for approval at the time of the first access, and you must support this new approach. Otherwise access is denied regardless of your manifest.

In Android 6.0, first you need to check for permission, then, if not granted, request it. The code examples can be found inside this SO question.

If you create files for exporting via USB cable to desktop using MTP protocol, may be a problem that newly created files are not immediately visible in the file explorer running on the connected desktop PC. To to make new files visible, you need to call MediaScannerConnection:

File file = new File(Environment.getExternalStoragePublicDirectory(
        Environment.DIRECTORY_DOCUMENTS), "theDocument.txt");
FileOutputStream out = new FileOutputStream(file)

... (write the document)

out.close()
MediaScannerConnection.scanFile(this, new String[] {file.getPath()}, null, null);
    context.sendBroadcast(new Intent(Intent.ACTION_MEDIA_SCANNER_SCAN_FILE,
            Uri.fromFile(file)));

This MediaScannerConnection call code works for files only, not for directories. The problem is described in this Android bug report. This may be fixed for some version in the future, or on some devices.

Small files are processed in a fraction of second and you can read / write them in place of the code where you need this. However if the file is bigger or otherwise slower to process, you may need to use AsyncTask in Android to work with the file in the background:

    class FileOperation extends AsyncTask<String, Void, File> {

        @Override
        protected File doInBackground(String... params) {
          try {
            File file = new File(Environment.getExternalStoragePublicDirectory(
            Environment.DIRECTORY_DOCUMENTS), "bigAndComplexDocument.odf");
            FileOutputStream out = new FileOutputStream(file)

           ... (write the document)

            out.close()
            return file;
            } catch (IOException ex) {
               Log.e("Unable to write", ex);
               return null;
              }
        }

        @Override
        protected void onPostExecute(File result) {
          // This is called when we finish 
        }

        @Override
        protected void onPreExecute() {
           // This is called before we begin
        }

        @Override
        protected void onProgressUpdate(Void... values) {
            // Unlikely required for this example
        }
    }
}

and then

new FileOperation().execute("Some parameters");    

This SO question contains the complete example on how to create and call the AsyncTask. Also see the question on error handling on how to handle IOExceptions and other errors.