only the Pear Mail for SMTP mail object supports authentication, the php mail() object does not.
if the email is not coming through, here are some things to check:
1) What did you enter for the smtp server name and port? in many cases, these can be left blank which use the php defaults, but some hosts will need this information entered, if you are not sure what to enter, contact your host.
2) What are you using for the from address? Many hosts will require that the from address be a valid address from your domain. If you are doing a contact form, you may want to set the Reply to address to use a dynamic email entered from the form, but use a static valid email from your domain as the actual from address.
3) Make sure not to use the same address for both the from address and the to address when testing. many hosts will consider this spam and not send the email.
if you need more details, i will need to know who your host is.
If you are sure everything is configured correctly and the email is still not coming through, you should contact the host to have them look into the smtp server error logs to see why the smtp server is not relaying the message.