Before you run tests, you'll want to ensure you run the composer install:
composer install
Now you'll want to ensure you have a local WP/DB set up. Once you confirm you have that done, you can setup your .env.local file. Copy the .env.example file to .env.local and fill in your local paths and DB connection information.
Copy the codeception.example.yml file to codeception.yml, and you're all set to run tests.
Running tests is pretty simple, you just run the codeception command codecept and which suite to run:
vendor/bin/codecept run wpunit -vvv
Running traversal tests requires use a different codeception test suite wpunit-traversal which makes use of special configuration files (see tests/codeception/_data/traversal-*.json). These tests have to be run apart from the other tests to prevent pollution of their configurations or data in the much more cleaner wpunit tests:
vendor/bin/codecept run wpunit-traversal -vvv
To run the JS tests, you'll want to first follow instructions to setup nvm/npm.
Once you have that setup, you can run the npm install:
npm install
Now you can run the tests:
npm run jest