In simple cases individual tests can be run by simply loading the page in a browser window. For running larger groups of tests, or running tests frequently, this is not a practical approach, and several better options exist.
For running multiple tests inside a browser, there is the test runner, located at
/tools/runner/index.html
This allows all the tests, or those matching a specific prefix (e.g. all tests under /dom/) to be run. For testharness.js tests, the results will be automatically collected, whilst the runner provides a simple UI for manually comparing reftest rendering and running manual tests.
Because it runs entirely in-browser, this runner cannot deal with edge-cases like tests that cause the browser to crash or hang.
For automated test running designed to be robust enough to use in a CI environment, the wptrunner test runner can be used. This is a test runner written in Python and designed to control the browser from the outside using some remote control protocol such as WebDriver. This allows it to handle cases such as the browser crashing that cannot be handled by an in-browser harness. It also has the ability to automatically run both testharness-based tests and reftests.
Full instructions for using wptrunner are provided in its own documentation.