1、检查是否有读写sdcard的权限

（1）首先要在AndroidManifest.xml加入

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

如果AndroidManifest.xml没有加入上面两条权限，是不可能进行动态权限申请的。动态权限申请，需要先在AndroidManifest.xml配置相应的权限。
（2）动态申请SD卡读写权限

    private void checkWriteAndReadPermission() {
        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.M) {
            if (checkSelfPermission(Manifest.permission.READ_EXTERNAL_STORAGE) == PackageManager.PERMISSION_DENIED ||
                    checkSelfPermission(Manifest.permission.WRITE_EXTERNAL_STORAGE) == PackageManager.PERMISSION_DENIED) {
                String[] permissions = new String[]{Manifest.permission.READ_EXTERNAL_STORAGE, Manifest.permission.WRITE_EXTERNAL_STORAGE};
                requestPermissions(permissions, 1000);
            }

        }
    }

    @Override
    public void onRequestPermissionsResult(int requestCode, @NonNull String[] permissions, @NonNull int[] grantResults) {
        super.onRequestPermissionsResult(requestCode, permissions, grantResults);
        for (int permission : grantResults) {
            if (permission == PackageManager.PERMISSION_DENIED) {
                Toast.makeText(this, "申请权限失败", Toast.LENGTH_LONG).show();
                break;
            }
        }
    }

2、创建文件目录

    private boolean createDir(String dir) {
        File fileDir = new File(dir);
        if (fileDir.exists() && fileDir.isDirectory()) {
            return true;
        } else {
            return fileDir.mkdirs();
        }
    }

3、创建文件

    private File createFile(String fileName) {
        File file = new File(fileDir, fileName);
        if (file.exists() && file.isFile()) {
            return file;
        } else {
            try {
                if (file.createNewFile()) {
                    return file;
                } else {
                    return null;
                }
            } catch (IOException e) {
                e.printStackTrace();
                return null;
            }
        }
    }

4、向文件写入数据

    private void write2File(File file, String data) {
        OutputStream ou = null;
        try {
            ou = new FileOutputStream(file);
            byte[] buffer = data.getBytes();
            ou.write(buffer);
            ou.flush();
            Toast.makeText(this,"写入成功",Toast.LENGTH_LONG).show();
        } catch (Exception e) {
            e.printStackTrace();
        } finally {
            try {
                if (ou != null) {
                    ou.close();
                }
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
    }

整个过程大概如此，Demo在Github上，欢迎下载学习。

谢谢阅读！