I find myself forgetting exactly what commands to run for the pytest test suite here. I think some kind of testing section in the readme just giving a few commands on how to test would be very useful.

I was running
pytest --pyargs cartopy.tests
or
pytest --pyargs cartopy.tests.specific_test_file.py
which I'm not even entirely sure is the best/right way to run the tests.

For example from matplotlib:
https://github.com/matplotlib/matplotlib#test
Maybe even a developer's guide page if you want to get really detailed?
https://matplotlib.org/devel/coding_guide.html#testing