At this point, the tests, support files and configuration files should be in their proper locations and you've changed the baseUrl to point to the site you want to target. If you want to run the registration test that verifies a registration email, don't forgot to set up Symfony Mailer. If you don't want to try that now, you can still run the all the tests—the first one will fail.
Cypress
You can launch the Cypress GUI in End-to-End mode with Firefox with this command:
npx cypress open --e2e --browser=firefox
Find the atk_register_login/atk_register_login.js file and click on it to run it. Be sure to set up Ethereal.mail and Drupal Symfony Mailer to verify that the site is sending email over the public internet (see Configuration).
Why Firefox? There is currently a bug with the cy.session() function on browsers other than Firefox. If you don't want to use the first test, add .skip to the test name (i.e. it.skip('(ATK-CY-1000) ...) and launch with another browser, like this:
npx cypress open --e2e --browser=electron
Refer to the excellent Cypress documentation or watch many of the tutorials online to learn Cypress.
Playwright
With Playwright, you can run the tests from within VS Code after you've installed the Playwright Test for VSCode plugin, which is an excellent way to write and debug Playwright tests. Here is a short tutorial on debugging within VS Code.
Or, you can launch the Playwright GUI with:
npx playwright test --ui
Refer to the very good Playwright documentation or the many tutorials online to learn Playwright.
After this section are references to the tests and functions of the Automated Testing Kit. Study the existing tests to see examples of how the functions are used. If you have questions, find me (André Angelantoni) on the Drupal Slack channel.