If the data you need is already unserialized, you don't need to do it again.
You will just need something like "$eventfields['fieldname']" in your template.
To find out which fields are in the array, TEMPORARY add the following line to your php-script, just after the unserialize:
PHP Code:
echo "<br />Eventfields: ";print_r($eventfields);
This wil show you the contents of the array.