Flarum extensions are Composer packages, so you can distribute/install them in many different ways supported by Composer.
If you have created an open-source extension, you can publish it on Packagist, the Composer-hosted package directory. We describe this method in our documentation https://docs.flarum.org/extend/distribution
Websites like Extiverse automatically scan Packagist for Flarum extensions to update their list of extensions. After publishing to Packagist you may create a discussion on this forum to make your extension known, though it's not required.
If you created a private extension just for yourself, you can install it on your forum through a local Composer repository. This is the same method used for developing extensions locally https://docs.flarum.org/extend/start#extension-packaging
Other methods include publishing paid extensions through Extiverse premium extension platform, Packagist.com, or hosting your own Satis-compatible endpoint for use with Composer.
If you're just trying to install an extension made by another developer on your forum, follow their instructions from the README file/discussion. You must be self-hosting your forum and have SSH/Composer access.