>>874662this
You need an outwards-facing unique IP address, so people can actually reach your machine and that's it. Set up a webserver on your box and serve up your site to the world. By default a visitor would need to know your IP. If you register a domain, you can put any IP you want into the name record (and change it whenever you want, as long as your registrar allows you direct access). That way you can point a domain to your local webserver.
If you have a dynamic IP you probably also have an asymmetric line, meaning your upload might be less than 1/10th of your download. You can immediately see how this would be unsuitable to host something for even a modest amount of visitors. But lots of people with beefy symmetric lines host their own stuff.