What is Drone? The official description is: "Drone is a Continuous Integration platform built on Docker".
What is Docker? Again, official description is :"Docker is an open-source project to easily create lightweight, portable, self-sufficient containers from any application".
10 minutes. This is all you need. In fact, there is an extra buffer in those 10 minutes to get your configuration working.
10 minutes is by order of magnitude less time than it would take you to get a Jenkins server up & running. I have never been a fan of Jenkins, and probably won't ever be, but let's keep this for another post, maybe.
We will assume that you have a Ubuntu 13.04 (64 bit) server with a routable IP or address. On Digital Ocean, which I love (referral here, thanks!), you can even have a VPS pre-built with Docker, 0.8 as of time of writing.
You can also use a Ubuntu 12.04 64 bit box in theory for Drone.
Your application needs to be hosted on GitHub. BitBucket coming soon apparently, but...