I click share and type the email address of the person and click invite but nothing happens.
I tried in the Notion app and on the website.
Nothing happens is hard to understand without knowing what are you expecting to happen.
I assume that the user is added to the Notion page you are sharing and if you click again on share, the user is actually there.
If by nothing happens you mean the user is not receiving an email with your invitation after 5 seconds, then yes, it can take minutes and not just 1, it can be 20 minutes, so it only takes patience.
If you already added someone, click the 3 dots at the top right, copy the page link and send them that, they will be able to see the page using their account.
Hope that helps.