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Generally, yes, you would contact your ISP to get a static IP address if you intend to host a site yourself.
Then, you'll need to decide whether you want to handle your own DNS, too.
If this is for a test site, then things are pretty simple. But if it's for an on-line site, then think about it a bit. What will you do about power outages? Who will watch the server while you sleep? What about vacations/holidays? And do you plan to get a second communications line from a different ISP installed, as a backup in case the first one fails? Are you confident in your ability to configure your server securely? If you have a technical problem, who will you call for help? All of these are usually handled by a hosting company, and that is part of what you pay for.
Also, make sure your ISP will *allow* you to set up a server on your account -- some won't.
Jim