The Survey module delivers surveys by email, so:
1. Have you added valid email addresses to the contacts in your group? If not, and your contacts have been in your account for a while, then you could export your group to .csv file, then add the email addresses onto your file then action an Update import of contacts using the Contact ID number (column on left) as the unique identifier. During this import remember to match the Contact ID field in the top section, tick Update in the Duplicate Processing section and also Contact ID as the unique identifier.
2. Have you added the contact preference for email onto your contacts? If not but their email addresses have been added, then you can run an Update Many on your group to add the email preference quickly across all the contacts in your group.
That should sort it but if you still have problems please raise a Support ticket to us.