Hi,
Can you see the e-mails on Sent tab of Site manager -> Administration -> E-mail queue?
(If there are no e-mails please check the settings: Site manager -> Settings -> E-mails -> Archive e-mails (days) to some number and send the testing newsletter once again.)
If you can see them it means they were sent from Kentico
CMS to SMTP server. There could be a problem with SMTP server (please check if From e-mail exists) or users can consider the newsletter as spam (please check the Spam box).
Best regards,
Helena Grulichova