Before doing this update you need to make sure your Drupal core is 8.8 or higher then follow the steps below:

1. Remove drupal-composer/drupal-scaffold from your project:

composer remove drupal-composer/drupal-scaffold

2. Modify your composer.json and remove any instant of drupal-scaffold located if your extra or scripts section like the following:
Note: The following does not work with the new scaffold project.

"drupal-scaffold": {
    "excludes": [ ".htaccess", "robots.txt" ]
},

3. Install the drupal/core-composer-scaffold by running the following command:

composer require drupal/core-composer-scaffold:^8.8 --no-update

4. You must define where the web root is located. It does so via the locations mapping, as shown below:

"extra": {
  "drupal-scaffold": {
    "locations": {
      "web-root": "./docroot"
    },
    ...
  }
}

5. You might prefer to entirely replace a scaffold file provided by a dependency, and receive no further updates for it. You can do this by adding the following:

"extra": {
  "drupal-scaffold": {
    "file-mapping": {
      "[web-root]/.htaccess": false
    }
  }
}

6. Run the following to update your lock file:

composer update --lock

7. If you are still using drupal/core in your composer.json, simply remove it and add drupal/core-recommended:

composer remove drupal/core
composer require drupal/core-recommended:^8.8