New order emails in Magento depend upon the cron job being setup. Check that your Magento cron job is setup properly. Ask your web host to set this up for you if you are not sure how to do it. Here is a page that shows how to do this:
Magento 1.9: http://support.xtento.com/wiki/Setting_up_the_Magento_cronjob
Magento 2.x: https://devdocs.magento.com/guides/v2.3/config-guide/cli/config-cli-subcommands-cron.html
** Note: By default - only customers get the order email. If you as the admin want to get the email too, go to
Magento 1.x: System > config > sales > sales emails and put your email address in the field "Send Order Email Copy To"
Magento 2.x: Store > config > sales > sales emails and put your email address in the field "Send Order Email Copy To"
