WordPress Internal email not working

I tried to register for a test site through my WP Register link to see if everything is working internally for a new user account.

Everything seemed ok and new user account details have been sent to registered email address. However, no email is being generated.

I installed a test email plugin which had said email has been sent but other than that carried very little other details.

What might I need to do here to set up and configure my emails so when a user registers etc, emails are sent out?

Thanks very much to all