You have to create a Google Search Console account and add your page, then typically you just drop a “marker” file in the root (Search Console generates this) so that Google can confirm you really own the page.
(Since the instructions are long and have many links to sub-steps, I’m only providing the link.)
Also, if you’re going to use a registered domain name, set that up before you register the site for search.
(Edit: Technically you don’t have to do this, sooner or later Google will find you… but this will give your content a much higher-quality score.)