WebPush is an open source library. Feel free to contribute by submitting a pull request or creating (and solving) issues!
First, you will need to create your own configuration file by copying phpunit.dist.xml to phpunit.xml and filling in the fields you need for testing (i.e. STANDARD_ENDPOINT, GCM_API_KEY etc.).
Then, download phpunit and test with one of the following commands:
For All Tests
php phpunit.phar
For a Specific Test File
php phpunit.phar tests/EncryptionTest.php
For a Single Test
php phpunit.phar . --filter "/::testPadPayload( .*)?$/" (regex)
Some tests have a custom decorator @skipIfTravis. The reason is that there's no way in Travis to update the push subscription, so the endpoint in my phpunit.travis.xml would ultimately expire (and require a human modification), and the corresponding tests would fail. But locally, these tests are handy.