You can check the basic mail functionality by entering your email address here and clicking the button. You should then receive a test email from "{senderEmailAddress}".
If no email is received, your setup might be broken. Check the following:
$GLOBALS['TYPO3_CONF_VARS']['MAIL']['transport']
is set to mail or sendmail, TYPO3 tries to use PHPs internal
mail() function. There might be no such program installed.
$GLOBALS['TYPO3_CONF_VARS']['MAIL']['transport']
is set to smtp, check if the data given in
$GLOBALS['TYPO3_CONF_VARS']['MAIL']['transport_smtp_*']
is valid. Wrong data here results in faulty requests to the
mail server. You can find the resulting messages in the mail server log.