If the subdomain will be hosted on the same droplet, then that is all you need for your DNS records. Using the wildcard, all subdomains will be directed to that IP address.
On the server side, you'll need to remember to specify ServerName in your Apache VirtualHosts so that the right content is served for each domain. For information on using VirtualHosts, check out:
The Apache web server is the most popular way to serve web content on the internet. Apache has the ability to serve multiple domains from a single server by using a mechanism called "virtual hosts". If a virtual host is configured correctly for each domain, the web server can correctly route traffic to the appropriate files based on the domain name requested. In this guide, we'll demonstrate how to configure Apache virtual hosts on an Ubuntu 14.04 VPS.