We have a number of security articles and tutorials that can walk you through securing your Droplet. You will need to take care of these actions yourself in order to prevent unauthorized access:

This article covers setting up a non-root user, and limiting root access
https://www.digitalocean.com/community/tutorials/initial-server-setup-with-ubuntu-14-04

This is an intro to Firewall article that links out to may other useful guides.
https://www.digitalocean.com/community/tutorials/what-is-a-firewall-and-how-does-it-work