在申请权限之前一定要在清单配置文件中添加该权限

private static final int MY_PERMISSIONS_REQUEST_RECORD_AUDIO = 1;  //随便定义

public void setPermission(){
    if (ContextCompat.checkSelfPermission(this,
            Manifest.permission.RECORD_AUDIO)  //这里申请的是录音权限
            != PackageManager.PERMISSION_GRANTED) {
        //没有权限的时候去申请
        ActivityCompat.requestPermissions(this,    
                new String[]{Manifest.permission.RECORD_AUDIO},
                MY_PERMISSIONS_REQUEST_RECORD_AUDIO);
    }else{
        //正常执行任务
    }
}

//权限请求结果

@Override
public void onRequestPermissionsResult(int requestCode, @NonNull String[] permissions, @NonNull int[] grantResults) {
    switch (requestCode){
        case MY_PERMISSIONS_REQUEST_RECORD_AUDIO :
            if (grantResults.length > 0 && grantResults[0] ==PackageManager.PERMISSION_GRANTED){
                //权限申请成功
            } else {
                //申请失败
                ToastUtils.show(this,"请到授权管理中开启");
            }
            break;
        default:
            break;

    }
}