Use the credentials Digital Ocean emailed you to connect to your Droplet via your computer's Terminal.

Once connected, type:

cd /var/www/

This will take you to where the Ghost files are actually installed.

Next, you'll need to directly download the new files from the URL you got earlier. Type (this may take a few seconds to download):

wget https://ghost.org/zip/ghost-0.6.4.zip

Now remove the old core directory by typing:

rm -rf ghost/core

Unzip the new files you've just downloaded by typing:

unzip -uo ghost-0.6.4.zip -d ghost

Make sure all of the files have the right permissions by typing in this command:

chown -R ghost:ghost ghost/*

Now, change into your Ghost directory with:

cd ghost

Then run this command to get any new dependencies:

npm install --production