The easiest way to run the tests is to invoke tox on the command line.
You will need to install the test requirements, which can be found in the setup.py file.
A good way to get started is to install the development version of the linter by doing pip install -e .[test].
To be able to fully test the linter, you will need both MySQL and PostgreSQL databases running.
You can either tweak the tests/test_project/settings.py file to get your DB settings right, or to have databases and users corresponding to the default CI users.
By default, the test Django project in the repository has multiple databases configured in order to make the CI tests work. Do not hesitate to modify the configured test databases.