Yes it is included.
By getting Droplet on DigitalOcean, you are getting VPS (Virtual Private Server) with root access. Root access is administrator rights on server, with that you bascically do whatever you want on server.
You are accessing Droplet via SSH, and you can learn how to do it in How To Connect To Droplet with SSH.
Your Droplet will include OS you selected on creation or you can select One-Click app which will include Ubuntu and selected apps already installed.
You can take a look at available apps on One-Click Apps page.
If you decide to go without One-Click app, DigitalOcean have great Tutorial base which will help you install any app.
In case you need help, ask here, we will try to help you :)
DigitalOcean Droplets are managed using a terminal and SSH. SSH is an encrypted network protocol for remote server login and command execution. It is the standard method used for accessing and interacting with Linux servers.
This tutorial shows how to connect to a DigitalOcean Droplet for the first time by using the OpenSSH client.