You need to begin with step 2 through this DigitalOcean tutorial page:

https://www.digitalocean.com/community/tutorials/how-to-set-up-a-host-name-with-digitalocean

Easy way to do it is just add the A record to your dns at godaddy pointing your your DO droplet ip.

See: http://support.godaddy.com/help/article/680/managing-dns-for-your-domain-names

Its been some time since I used Godaddy and never liked the screwed up way they do the control panel.