Simply enter your D.O. client credentials at the top of the script. Set the domain you want to update and the 'Record' for that domain and schedule the script to run however often you want (using for example the Windows Scheduler or a cron job).
My home server has a sticky IP, I want to be able to connect to it remotely using:
I'd create an 'A' record in DO with the hostname 'home', under the domain 'joebloggs.co.uk' and while I was there retrieve my API credentials.
If you're using the python or updater.php script you'll need a (client ID & key, v1 of the API). If however your using the v2 of the API (updater-v2.php and recommended) then you'll need to generate a 'Personal Access Token'.