You'll need SSH access. Once you SSH into your server, and navigate to the directory your flarum is installed in (hint, it should be possible to run php flarum info and get back a successful message). Then you simply run:
composer require vendor/flarum-ext-name
That's an example, but every extension will provide its specific name to use. For example, my summaries mod would be jordanjay29/flarum-ext-summaries. You can usually find the entire installation commands in any thread in the Extensions tag here on our site.
If you do not have SSH access on your server, you'll have a much harder time. Others have accomplished this, but it's time-consuming, and requires having a local mirror of your Flarum installation on a localhost (like XAMPP).
