Can't get WRITE_SETTINGS permission

To use WRITE_SETTINGS, based on the docs:

1. Have the <uses-permission> element in the manifest as normal.

2. Call Settings.System.canWrite() to see if you are eligible to write out settings.

3. If canWrite() returns false, start up the ACTION_MANAGE_WRITE_SETTINGS activity so the user can agree there to allow your app to actually write to settings.

In other words, writing to settings is now a double-opt-in (agree to install, agree separately in Settings to allow), akin to device admin APIs, accessibility services, etc.

Also note that I have not tried using these yet — this is based on research that I did yesterday on Android 6.0 changes.

In addition to the answer from CommonsWare and the comment from Ogix, here is some dummy code:

private boolean checkSystemWritePermission() {
    boolean retVal = true;
    if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.M) {
        retVal = Settings.System.canWrite(this);
        Log.d(TAG, "Can Write Settings: " + retVal);
        if(retVal){
            Toast.makeText(this, "Write allowed :-)", Toast.LENGTH_LONG).show();
        }else{
            Toast.makeText(this, "Write not allowed :-(", Toast.LENGTH_LONG).show();
            FragmentManager fm = getFragmentManager();
            PopupWritePermission dialogFragment = new PopupWritePermission();
            dialogFragment.show(fm, getString(R.string.popup_writesettings_title));
        }
    }
    return retVal;
}

The Fragment PopupwritePermission then gives a window where the situation is explained. A click on the OK Button will open the Android System Menu where the Permission can be granted:

private void openAndroidPermissionsMenu() {
    Intent intent = new Intent(Settings.ACTION_MANAGE_WRITE_SETTINGS);
    intent.setData(Uri.parse("package:" + getActivity().getPackageName()));
    startActivity(intent);
}

The previous answers are great, I have just little addition for also getting the result for the permission asking.

 public static void youDesirePermissionCode(Activity context){
        boolean permission;
        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.M) {
            permission = Settings.System.canWrite(context);
        } else {
            permission = ContextCompat.checkSelfPermission(context, Manifest.permission.WRITE_SETTINGS) == PackageManager.PERMISSION_GRANTED;
        }
        if (permission) {
            //do your code
        }  else {
            if (android.os.Build.VERSION.SDK_INT >= android.os.Build.VERSION_CODES.M) {
                Intent intent = new Intent(Settings.ACTION_MANAGE_WRITE_SETTINGS);
                intent.setData(Uri.parse("package:" + context.getPackageName()));
                context.startActivityForResult(intent, MainActivity.CODE_WRITE_SETTINGS_PERMISSION);
            } else {
                ActivityCompat.requestPermissions(context, new String[]{Manifest.permission.WRITE_SETTINGS}, MainActivity.CODE_WRITE_SETTINGS_PERMISSION);
            }
        }
    }

And then in the Activity:

@SuppressLint("NewApi")
    @Override
    protected void onActivityResult(int requestCode, int resultCode, Intent data) {
        super.onActivityResult(requestCode, resultCode, data);
        if (requestCode == MainActivity.CODE_WRITE_SETTINGS_PERMISSION && Settings.System.canWrite(this)){
            Log.d("TAG", "MainActivity.CODE_WRITE_SETTINGS_PERMISSION success");
            //do your code
        }
    }

    @Override
    public void onRequestPermissionsResult(int requestCode, @NonNull String[] permissions, @NonNull int[] grantResults) {
        super.onRequestPermissionsResult(requestCode, permissions, grantResults);
        if (requestCode == MainActivity.CODE_WRITE_SETTINGS_PERMISSION && grantResults[0] == PackageManager.PERMISSION_GRANTED) {
            //do your code
        }
    }