1. Check Global Configuration settings.
a. Make sure sending mail is enabled on site. Go to Global Configuration->Server and look at Mail section in bottom right. Make sure the SEND MAIL toggle is set to YES.
b. Make sure other email information is filled in.
2. Send Test Email: Go to Global Configuration->Server and look at Mail section in bottom right. If you do not have access to the email listed, temporarily change it to one you do. Then hit the new SEND TEST MAIL button added in Joomla 3.x.
3. Make sure the email address is valid and a real email address not a distribution list. You might want to try some other email addresses you have access to determine where the issue is.
To test specific mail settings, you need to...