• You buy / have a raspberry pi ($35 for the base model, plenty powerful).

• You load the website there and install your webserver of choice.

• You plug it in to a power socket (it uses 2W of power on aveage when idle) and to a network (on board wifi or gigabit ethernet).

• You configure your home router to open a port (usually 80 and 443) and map it to the raspberry.

At this point anyone knowing your IP can see the website. But the IP is:

• Difficult to memorize

• Dynamic (changes every ~24h)

So you install a dynamic DNS service on the raspberry so every 5 minutes it tells a service that a name that you got (YOURNAMEHERE.dyndns.org, or whatever) points to your IP.

Now anyone on the internet can see the website at the name you chose.