Well, do you know for sure that you do not already have wildcarded DNS for your subdomains?
To check, go to
http://gfsfgasdgsdafasgas.yourdomain.com or an unexisting subdomain on your server.
If some sort of response from the server appears as a page saying Apache (or the type of server you're using) has been configured, or something to that degree, you have wildcarded DNS already.
If this does not work, please contact your system administrator. they will help you resolve your issue.
If it does work, you are going to have to find the entry for your domain name. Right after your domain name, you are going to want to make sure other entries for other domains come before the wildcarded domains, so the wildcard doesn't override the true subdomains. The httpd.conf file can usually be found at /usr/local/apache/conf/httpd.conf on cPanel servers.
The following code can be placed in your httpd.conf file (granted you have access to it. It can be found on the path listed above. If you do not have access or are having trouble finding it, you need to contact your system administrator).
Then make sure you save httpd.conf followed by a restart of httpd.
Good :gl: Luck and happy Wildcarded DNS
-Steve