In the past, I was able to access a free service from dyndns.com, which connected to my server which had a dynamically-assigned IP address. My server had a service running which, every minute or so, updated dyndns.com with the current IP address.
This avoided my need to have a static IP address for my website.
Do you know of any equivalent service that's still available for free?
At the moment, dyndns.com redirects to dyn.com/dns ... and they want $5 per month. I guess that's not really all that much.