Unfortunately there is no easy answer. DigitalOcean does not currently provide DDoS protection services so you will not be able to protect your service without using a third party solution. For web applications, CloudFlare provides an easy free solution for this. For UDP connections to game servers you will have to look into whether there is a suitable reverse-proxy service that provides the protection you need.

We understand that protection from DDoS attacks is an important feature and is one thing that our teams are seriously looking into but we don't have an ETA for this type of service currently.