Here are the steps required to allow a non-Google user access to a Google Site.

1. Open the edit page of the Google Site.  Select the Share with others button

2. Enter the email address that you want to grant access to the site

3. Finish entering the information. Be sure that permissions are set to "Published Viewer".  You can include an optional message to the recipient.  Also, be sure the "Notify people" checkbox is checked.  Click "Send"

The next steps are very important to guarantee that the user can properly authenticate and access the site.  

4. The invitee will receive an email with a button to open the site and go through the verification process.  They should click "Open"

5. Their web browser will open and they will see the following message.  They should click "Send"

6. They will see the following message. Once the verification code is sent to their email, they should enter it in the box and click "Next"

7. The website will open for viewing