使用以下代码打开一个对话框：

 ActivityCompat.requestPermissions(MainActivity.this,
                    new String[]{Manifest.permission.READ_EXTERNAL_STORAGE},
                    1);

获取活动结果如下：

@Override
public void onRequestPermissionsResult(int requestCode,
                                       String permissions[], int[] grantResults) {
    switch (requestCode) {
        case 1: {

          // If request is cancelled, the result arrays are empty.
          if (grantResults.length > 0
                    && grantResults[0] == PackageManager.PERMISSION_GRANTED) {

                // permission was granted, yay! Do the
                // contacts-related task you need to do.          
            } else {

                // permission denied, boo! Disable the
                // functionality that depends on this permission.
                Toast.makeText(MainActivity.this, "Permission denied to read your External storage", Toast.LENGTH_SHORT).show();
            }
            return;
        }

        // other 'case' lines to check for other
        // permissions this app might request
    }
}

更多信息：https
://developer.android.com/training/permissions/requesting.html