I found the following worked for me. This is simple to do and quite quick to setup.

Source: http://ubuntuhandbook.org/index.php/2015/01/remotely-access-graphical-desktop-of-ubuntu-14-04-server/

Your Droplet
The source recommends creating your droplet with a hostname, but I don’t see the utility. Anyway, after creation, ssh in and execute the following:

# For this first line, I was having issues with the digitalocean ubunutu mirrors and switched them out.  This may not be neccessary if digitalocean fixes the issues later.
sudo sed 's/mirrors.digitalocean.com/mirror.us.leaseweb.net/g' -i /etc/apt/sources.list
sudo apt-get update
sudo apt-get install python-software-properties software-properties-common -y
sudo apt-add-repository -y ppa:x2go/stable
sudo apt-get update
sudo apt-get install x2goserver x2goserver-xsession -y
sudo apt-get install xfce4 -y #optional
reboot

Locally
You’ll need to do this (assuming you’re on ubuntu/mint, but probably works on any debian as well):

sudo apt-add-repository ppa:x2go/stable
sudo apt-get update
sudo apt-get install x2goclient

Now, start your x2go and create a new session:

• hostname: ip address of your droplet
• username: probably root
• assuming you are using ssh keys, just check the box to use default key
• Optionally disable print sharing or else you might get a warning when starting the session, but you can also just ignore the error message.
• start your session in x2go. BOOM! Done. Start installing apps or whatever…

This is a super basic setup that may not work for everyone. In my case, I have crap bandwidth and needed a place to download a few gigs of data, massage it with csvkit, awk, etc and reupload without it taking hours and hours for data transfers.