You will firstly need to retrieve the user ID like so:
$id = JFactory::getUser()->id;
Then get the array of profile data, like so:
$profile = JUserHelper::getProfile($id)->profile;
You can now access any of the data:
echo $profile['address1'];
echo $profile['address2'];
echo $profile['city'];
echo $profile['region'];
echo $profile['country'];
echo $profile['postal_code'];
echo $profile['phone'];
echo $profile['website'];
echo $profile['favoritebook'];
echo $profile['aboutme'];
echo $profile['dob'];
You need to make sure you're logged in, else you won't be able to get the information:
Here's the full code with a sanity check:
$user = JFactory::getUser();
if (!$user->guest)
{
$profile = JUserHelper::getProfile($user->id)->profile;
echo $profile['address1'];
echo $profile['address2'];
echo $profile['city'];
echo $profile['region'];
echo $profile['country'];
echo $profile['postal_code'];
echo $profile['phone'];
echo $profile['website'];
echo $profile['favoritebook'];
echo $profile['aboutme'];
echo $profile['dob'];
}