Just recording a few of these steps for future reference.
Pull the MySQL image from the hub:
docker pull mysql/mysql-server:latest
Run an instance:
docker run -it -d -p 33060:3306 --name mysql-for-jonny -e MYSQL_ROOT_PASSWORD=opensesame -d mysql/mysql-server:latest
Run a shell on the instance:
docker exec -it mysql-for-jonny /bin/bash
Once inside the instance use the MySQL client:
mysql -u root -popensesame
and create a new user:
GRANT ALL PRIVILEGES ON *.* TO jonny@'%' IDENTIFIED BY 'letjonnyin';
Quit the MySQL client and exit the instance. From the host system try connecting to MySQL on the instance:
mysql -u jonny -pletjonnyin -h localhost --protocol=tcp --port 33060
Now that instance of MySQL can be inspected from the host.