Normally the live database would not be exposed publicly as this a security risk, and may be hosted on a different machine to your website.
If it is exposed the syntax would be something like:
mysql -u username -p dbserver.example.com dbname
You'll be prompted for the password.
That said.. why do you want to connect from your local?
hosts typically provide a HTML UI to access the database,
or you should ssh in and use the command line client from there.