Since the new version of drush has come out and now requires Composer, most of the guides I've seen online don't work anymore. Hopefully, this guide will prevent others from the headaches I went through getting this setup on my host.
First, I'm assuming you already have SSH access to your host. If not, go get that done and come back to install drush. It will be a little different depending on your hosting provider.
Make sure you're in your home directory